what is a paper quantity

Paper Quantities - Quire, Ream, Bundle, Bale & Pallet

When buying paper it is useful to know how much you are getting for your money, paper is normally sold to the consumer in reams or quires and commercially in bundles, bales and more recently pallets. In modern times the ream has become standardised at 500 sheets and the quire at 25 sheets.

Modern (Metric) Paper Quantities

The following table gives the number of sheets for each of the quire, ream, bundle and bale (pallets are covered further down the page).

Ream of 80gsm office paper.

Pallets of Paper

In the US a pallet of paper is usually 40 cases of 10 reams per case giving a total of 200,000 sheets. In the UK a pallet can be either 20 boxes of 5 reams per box (50,000 sheets) or 50 boxes of 5 reams (125,000 sheets) depending upon who you purchase from.

Other Paper Quantities

It is fairly common these days to see specialist papers sold in 100 sheet (4 quire) packages and heavier weight card (160gsm+) being sold in 250 sheet (10 quire) packages.

Imperial Reams & Quires

Prior to standardisation on the metric ream and quire of 500 and 25 sheets respectively, the UK and other British Commonwealth countries used a quire of 24 sheets (2 dozen) and a ream of 20 quires at 480 sheets. This was also used in the US where it is known as the short quire.

The following table gives the number of sheets for the Imperial (Short) quire, ream, bundle and bale.

Imperial Ream & Quire Sizes - An excerpt from Everybody's Pocket Companion Published by T.V. Boardman & Co. Ltd in late 1939 to early 1940.

The Printer's Ream

The printer's ream of 516 sheets was used, before the standardisation on 500 sheet reams, when purchasing paper to ensure that wastage during the print process did not leave the finished job short of a standard ream (e.g. when producing headed paper for typing that would have been ordered by the ream).

Weight of Sheets & Reams Calculator

More information on paper weights can be found here .

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Definition of ream

(Entry 1 of 2)

Definition of ream (Entry 2 of 2)

transitive verb

lashings [ chiefly British ]
lashins
multiplicity
hose [ slang ]
nobble [ British slang ]
shortchange

Examples of ream in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'ream.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Middle English reme , from Anglo-French, ultimately from Arabic rizma , literally, bundle

perhaps from Middle English *remen to open up, from Old English rēman ; akin to Old English rȳman to open up, rūm space — more at room

14th century, in the meaning defined at sense 1

1815, in the meaning defined at sense 1a

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Cite this Entry

“Ream.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/ream. Accessed 3 Jun. 2024.

Kids Definition

Kids definition of ream.

Kids Definition of ream (Entry 2 of 2)

Middle English reme "a quantity of paper," from early French reme (same meaning), from Arabic rizma, literally, "bundle"

probably from Old English rēman "to open up"

More from Merriam-Webster on ream

Nglish: Translation of ream for Spanish Speakers

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Measuring Distance

How to Measure Paper

Last Updated: May 18, 2020 References

This article was reviewed by Anne Schmidt . Anne Schmidt is a Chemistry Instructor in Wisconsin. Anne has been teaching high school chemistry for over 20 years and is passionate about providing accessible and educational chemistry content. She has over 9,000 subscribers to her educational chemistry YouTube channel. She has presented at the American Association of Chemistry Teachers (AATC) and was an Adjunct General Chemistry Instructor at Northeast Wisconsin Technical College. Anne was published in the Journal of Chemical Education as a Co-Author, has an article in ChemEdX, and has presented twice and was published with the AACT. Anne has a BS in Chemistry from the University of Wisconsin, Oshkosh, and an MA in Secondary Education and Teaching from Viterbo University. This article has been viewed 34,767 times.

You’d be surprised at how often you may need to know the measurements of a single piece of paper! Whether you’re needing to get a frame for a special document or photo or are trying to make sure the thickness of a piece of paper will be enough to hold a certain type of ink or paint, measuring paper can be a useful skill. At the very least, you’ll need a ruler and something to jot down your measurements with. Once you know what you’re doing, it’ll just take you a minute to get the measurements you need.

Figuring out the Thickness of Paper

Step 1 Measure the height of stacked sheets of paper with a ruler.

For example, if you stack together 50 sheets of paper and find out they measure 1 ⁄ 4 inch (6.4 mm) in height, divide .25 by 50. Each piece of paper is .005 inches (0.13 mm) thick.

Finding the Volume of a Sheet of Paper: If you need to know the volume for a particular sheet of paper, multiply the length times the width times the height (or, the thickness of the sheet of paper). For example, the volume of an 8.5 by 11 in (220 by 280 mm) piece of paper that measures .005 inches (0.13 mm) thick is found by multiplying 8.5 x 11 x .0005 , which equals 0.4675 cubic inches (7660 cubic millimeters).

Step 2 Fold a sheet of paper multiple times if you don’t have a stack to measure.

For this method, it’s especially important that you get your folds to lay as flat as possible. You may want to stack a book on top of the paper or do something else to weigh it down so your measurement is accurate.
If you’re worried about the creases and folds messing up your measurements, you could cut the paper into multiple pieces and stack them on top of each other instead.

Step 3 Get a precise reading on a single sheet of paper by using a micrometer.

Always check your particular micrometer’s instructions to make sure it has been set up correctly.
A micrometer can give you a measurement reading to the one-thousandth of an inch, which is really impressive and important if you need specific details!
You could also use a dial caliper or vernier caliper to get the same results.

Measuring Length and Width

Step 1 Lay out the piece of paper so that it is completely flat.

Measuring the length and width of a piece of paper can come in handy if you’re trying to purchase the right size frame for a picture or if you need to buy a folder or display case.

Step 2 Use a ruler to measure the length of the paper from top to bottom.

Use a ruler that includes both inches and centimeters so you can get the most accurate reading possible.

Step 3 Place a ruler along the short edge of the paper to measure the width.

Be sure to keep the edge of the ruler and the edge of the piece of paper together. Otherwise, the measurement won’t be accurate.

Step 4 Write down the measurements on a piece of paper.

To write the measurements, put the width and then the height. For example, a normal piece of printer paper is 8.5 by 11 inches (220 by 280 mm).

Expert Q&A

The thickness and size of a piece of paper may be especially important if you’re working on a craft project or if you’re printing something special. Really thin paper might not hold certain types of ink or paint very well, or you might need a specific size to fit a particular frame. Thanks Helpful 1 Not Helpful 0

Things You’ll Need

Micrometer (optional)

↑ https://sciencing.com/find-volume-piece-paper-4474948.html
↑ https://spark.iop.org/measuring-paper
↑ https://www.hamblyscreenprints.com/thickness-of-paper/
↑ https://www.thepaperframer.com/measure.php
↑ https://sciencing.com/measure-length-width-6556796.html

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Units of paper quantity

Various measures of paper quantity have been and are in use. Although there are no S.I. units such as quires or bales , there are ISO [1] and DIN [2] standards for the ream . Expressions used here include U.S. Customary Units .

Etymology 2

Explanatory notes

External links.

The current word quire derives from Old English quair or guaer , from Old French quayer , cayer , (cf. modern French cahier ), from Latin quaternum , 'by fours', 'fourfold'. Later, when bookmaking switched to using paper and it became possible to easily stitch 5 to 7 sheets at a time, the association of quaire with four was quickly lost.

In the Middle Ages, a quire (also called a " gathering ") was most often formed of four folded sheets of vellum or parchment , i.e. eight leaves, 16 sides. The term quaternion (or sometimes quaternum ) designates such a quire. A quire made of a single folded sheet (i.e. two leaves, four sides) is a bifolium (plural bifolia ); a binion is a quire of two sheets (i.e. four leaves, eight sides); and a quinion is five sheets (ten leaves, 20 sides). This last meaning is preserved in the modern Italian term for quire, quinterno di carta .

Formerly, when paper was packed at the paper mill , the top and bottom quires were made up of slightly damaged sheets ("outsides") to protect the good quires ("insides"). These outside quires were known as cassie quires (from French cassée , 'broken'), or "cording quires" and had only 20 sheets to the quire. [10] The printer Philip Luckombe in a book published in 1770 mentions both 24- and 25-sheet quires; he also details printer's wastage, and the sorting and recycling of damaged cassie quires. [11] An 1826 French manual on typography complained that cording quires (usually containing some salvageable paper) from the Netherlands barely contained a single good sheet. [12] [Note 1]

It also became the name for any booklet small enough to be made from a single quire of paper. Simon Winchester , in The Surgeon of Crowthorne , cites a specific number, defining quire as "a booklet eight pages thick." Several European words for quire keep the meaning of "book of paper": German Papierbuch , Danish bog papir , Dutch bock papier .

In blankbook binding, quire is a term indicating 80 pages.

A ream of paper is a quantity of sheets of the same size and quality. International standards organizations define the ream as 500 identical sheets. [1] [2] [Note 2] This ream of 500 sheets (20 quires of 25 sheets) is also known as a 'long' ream, and is gradually replacing the old value of 480 sheets, now known as a 'short' ream. Reams of 472 and 516 sheets are still current, [13] but in retail outlets paper is typically sold in reams of 500. As an old UK and US unit, a perfect ream was equal to 516 sheets. [9]

Certain types of specialist papers such as tissue paper, greaseproof paper, handmade paper, and blotting paper are still sold (especially in the UK) in 'short' reams of 480 sheets (20 quires of 24 sheets). However, the commercial use of the word 'ream' for quantities of paper other than 500 is now deprecated by such standards as ISO 4046. [1] In Europe, the DIN 6730 standard for Paper and Board includes a definition of 1 ream of A4 80 gsm (80 g/m 2 ) paper equals 500 sheets. [2]

The word 'ream' derives from Old French reyme , from Spanish resma , from Arabic rizmah 'bundle' (of paper), from rasama , 'collect into a bundle'. (The Moors brought manufacture of cotton paper to Spain.) The early variant rym (late 15c.) suggests a Dutch influence. [14] (cf. Dutch riem ), probably during the time of Spanish Habsburg control of the Netherlands .

The number of sheets in a ream has varied locally over the centuries, often according to the size and type of paper being sold. Reams of 500 sheets (20 quires of 25 sheets) were known in England in c. 1594; [15] in 1706 a ream was defined as 20 quires, either 24 or 25 sheets to the quire. [16] In 18th- and 19th-century Europe, the size of the ream varied widely. In Lombardy a ream of music paper was 450 or 480 sheets; in Britain, Holland and Germany a ream of 480 sheets was common; in the Veneto it was more frequently 500. Some paper manufacturers counted 546 sheets (21 quires of 26 sheets). [17] J. S. Bach 's manuscript paper at Weimar was ordered by the ream of 480 sheets. [18] In 1840, a ream in Lisbon was 17 quires and three sheets = 428 sheets, and a double ream was 18 quires and two sheets = 434 sheets; and in Bremen , blotting or packing paper was sold in reams of 300 (20 quires of 15 sheets). [19] A mid-19th century Milanese -Italian dictionary has an example for a risma (ream) as being either 450 or 480 sheets. [20]

In the UK in 1914, paper was sold using the following reams: [21]

472 sheets: mill ream (18 short quires of 24 sheets of 'insides', two cording quires of 20 sheets of 'outsides')
480 sheets: (20 short quires of 24 sheets) – now called 'short' ream (as an old UK and US measure, in some sources, a ream was previously equal to 480 sheets) [9]
500 sheets: (20 quires of 25 sheets) – now also called 'long' ream
504 sheets: stationer's ream (21 short quires)
516 sheets: printer's ream (21½ short quires) – also called 'perfect ream'

Reams of 500 sheets were mostly used only for newsprint. [21] Since the late 20th century, the 500-sheet ream has become the de facto international standard.

A paper bundle is a quantity of sheets of paper, currently standardized as 1,000 sheets. A bundle consists of two reams or 40 quires. As an old UK and US measure, it was previously equal to 960 sheets. [9]

When referring to chipboard , there are two standards in the US. In general, a package of approximately 50 pounds of chipboard is called a bundle. Thus, a bundle of 22 point chipboard (0.022" thick) 24" × 38", with each sheet weighing 0.556 pounds, contains 90 sheets. However, chipboard sold in size 11" × 17" and smaller is packaged and sold as bundles of 25 pounds.

A paper bale is a quantity of sheets of paper, currently standardized as 5,000 sheets. A bale consists of five bundles, ten reams or 200 quires. [22] As an old UK and US measure, it was previously equal to 4800 sheets. [9]

History of paper
History of printing
Paper density
↑ A note on the flyleaf of this copy states that this edition was pirated from Didot's 1st ed. of 1825; see pp. 235–236, especially in respect of the examples of proof-reader's corrections on pp. 162–163
↑ ISO 4046 (see References) defines the ream as "a pack of 500 identical sheets of paper" and appends a note: "In many countries it is common practice to use the term "ream" for other quantities, for example 480 sheets, thus affecting the quire. For quantities other than 500 sheets, a different term, such as "pack", should be used."

Paper Weight Calculator

Table of contents

This paper weight calculator will help you determine the weight of a sheet of paper of any size, grammage, or basis weight . You can also use this calculator for paper weight conversion between grammage and basis weight and to find what the grammage of paper is.

In this calculator, you will learn about the measure of weight per unit area that is used to determine the weight of paper, as well as what the basis weight of paper is. We will also show you a paper weight chart that you can use as a paper weight guide for your prints. So, how do you calculate paper weight? Let's find out!

💡 Need to print a large-scale photo but not sure if your photo resolution will be enough? You can use our pixels to print size calculator to help you find out.

Paper weight chart: What is the grammage of paper?

Paper comes in a variety of sizes, colors, textures, thicknesses, and weights. In this paper weight calculator, we focus on the weight of paper sheets and how we calculate them. To keep it a standard among manufacturers and consumers, we use a certain unit of measure. This is called grammage .

Grammage is a paper's weight in terms of grams per square meter (g/m²) . This unit is also commonly abbreviated to gsm , and you can usually see this printed on the paper's packaging.

What does paper weight mean?

Not only does grammage define the weight of a sheet of paper, but it also tells us something about the stiffness of a paper sheet . The higher the grammage, the stiffer and the heavier the paper is. A good thing to note is that though grammage defines the paper sheet's weight, it doesn't necessarily describe its thickness.

🙋 You can check out our paper thickness calculator if you want to learn about paper thickness.

Typical office papers are usually around 75-120 gsm, while photo papers are generally around 180-240 gsm. Heavier papers or cardstocks of about 250-350 gsm are best for invitations, event programs, postcards, and business cards. However, the choice of grammage still depends on personal preference and creative choices. As a paper weight guide on choosing the suitable grammage for your prints and other usages, we have here a paper weight chart for your reference:

Chart showing the suitable grammage for various uses of paper.

Basis weight of paper

Aside from the paper weight meaning that we've shown you so far, i.e., grammage, we also have the basis weight unit of measure as a reference in determining the weight of a paper sheet. Basis weight is the weight in pounds of a ream, or 500 sheets of paper, at particular basic sheet sizes , which vary depending on the stock type of paper being considered.

The different stock types are bond, text, tag, index, Bristol, and cover stock paper. The paper weight conversion table below shows their estimated common basis weights in pounds and equivalent weights in grammage. Additionally, in the first row, you can find their corresponding basic sheet sizes.

For example, from the table above, we can see a 20 lb bond stock paper , a 50 lb text stock paper , and a 75 gsm paper , when cut to the same size, will have approximately the same weight.

Now that we know what grammage and basis weight is, let us now learn how to calculate the paper weight.

How do you calculate paper weight?

Since grammage is a unit of weight per unit of area, we have to multiply the paper's area by its grammage to find the paper sheet's weight. And since the area of a rectangular paper sheet is simply the product of its length and width, we can then formulate the equation for the weight of a paper sheet as follows:

weight \text{weight} weight — Weight of a paper sheet;
L L L — Length of the sheet of paper;
W W W — Width of the sheet of paper; and
g g g — Paper grammage.

On the other hand, calculating the paper weight using the basis weight has quite similar procedures. We need to multiply the basis weight by the paper sheet area in question and divide it by the appropriate basic sheet area multiplied by 500. In equation form, we can express it as shown below:

b b b — Basis weight; and
A basic A_\text{basic} A basic — Basic sheet area.

For multiple sheets of paper, we can multiply the weight of a paper sheet by the paper quantity, n \small n n , to calculate the total weight, W total \small W_\text{total} W total , of the paper, as shown in the equation below:

✅ We have different names for different numbers of paper sheets, like reams, bundles, or bales. Learn more about them in our paper quantity converter .

Using our paper weight calculator

Here are the steps on how to use our paper weight calculator:

Select the unit of measure you want to use , either grammage or basis weight.

If you selected grammage , enter the grammage value and proceed to step 4.

If you selected basis weight , choose the appropriate basic sheet size and enter your paper's corresponding basis weight .

Next step is to select or input the paper size of your paper .

Upon entering your paper's dimensions, you will then see the weight per sheet .

Change the value in the Quantity field to match your requirements to find the total weight you need.

To use our calculator for paper weight conversion, select "basis weight" in the Units field and follow the steps below:

To convert a basis weight to grammage , select a basic sheet size and enter a basis weight. This will then display an equivalent grammage.

To convert grammage to basis weight , enter a grammage value first. Then choose your desired basic sheet size. This will then result in a value for the basis weight.

To convert a basis weight to another basis weight , simply select "Yes" in the Convert to another basis weight? field. This will reveal two more fields where you can choose the new basic sheet size you wish to convert to and see the value of the basis weight for that stock type.

Sample calculation of the weight of paper

Let's say we are asked to purchase five reams (2,500 sheets) of 70 gsm A4 size copy paper for the office, and we want to know how much it weighs. An A4 size paper has a width of 0.210 m and a length of 0.297 m . Since we already have all the necessary dimensions, we can now find the weight of our paper by substituting these values into our formula:

Multiplying this value by the 2 , ⁣ 500 \small 2,\!500 2 , 500 , which is the total quantity of paper sheets in five reams, we obtain the total weight of paper that we want to know, as shown below:

We also use a similar procedure in determining the weight of similarly-shaped objects like metal sheets and plates. If you find this topic interesting and would love to learn more, you can also visit our steel plate weight calculator or our log weight calculator – which uses a different procedure of weight calculation.

How much does a sheet of paper weigh?

This value is dependent on the paper.

What is gsm in paper weight?

Gsm is a unit of measurement that means grams per square meter . It tells you how many grams a square meter of paper weighs. It is often referred to as grammage. For reference, 1 gsm = 0.67 lbs .

How should I calculate the weight a sheet of paper?

To calculate the weight of a sheet of paper , follow these steps:

Get the grammage of the paper: say 55 gsm .

Get the area of the paper: 0.0625 m² .

Use the paper size formula:

weight = area × grammage

Substitute the values:

weight = 0.0625 × 55 weight = 3.4375 g

What weight is copy paper?

Copy paper varies in size, grammage, and area. Two popular sizes are letter ( 8.5 x 11 inches ) and legal ( 8.5 x 14 inches ). Some legal-size copy papers are 75 gsm . The weight of this legal size paper is 5.758 g :

To calculate this, we use the formula:

Weight = Area × grammage

Because grammage is expressed in grams per meter square and the dimensions are in inches, we need to multiply by 0.0254² to express this value in meters.

Weight = (8.5 × 14 × 0.0254²) × 75

Weight = 5.758 g

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Select between grammage or basis weight depending on your preference.

Basic sheet size

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Basis weight (of a ream)

Weight of a ream (500 sheets) of your selected reference basic sheet size in pounds.

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Equivalent weight of paper in grams per square meter.

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Output values

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A quantity of paper, 20 quires . Abbreviation, rm. Well into the 20th century a ream of writing paper contained 480 sheets and a ream of printing paper was 500 sheets, while suppliers of printers and publishers used a ream of 516 sheets. Today the standard ream of all types of paper is 500 sheets.

One sometimes sees it stated that 1 printer’s ream = 21½ quires.¹ If so, these are ordinary 24-sheet quires, not printer’s quires of 25 sheets.

1. for example, Alfred J. Martin. Up-to-date Tables of Imperial, Metric, Indian and Colonial Weights and Measures… London: T. Fisher Unwin, 1904 . Page 191.

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1.3 The Language of Physics: Physical Quantities and Units

Section learning objectives.

By the end of this section, you will be able to do the following:

Associate physical quantities with their International System of Units (SI)and perform conversions among SI units using scientific notation
Relate measurement uncertainty to significant figures and apply the rules for using significant figures in calculations
Correctly create, label, and identify relationships in graphs using mathematical relationships (e.g., slope, y -intercept, inverse, quadratic and logarithmic)

Teacher Support

The learning objectives in this section will help your students master the following standards:

(H) make measurements with accuracy and precision and record data using scientific notation and International System (SI) units;
(L) express and manipulate relationships among physical variables quantitatively, including the use of graphs, charts, and equations.

In addition, the High School Physics Laboratory Manual addresses content in this section in the lab titled: Measurement, Precision and Accuracy, as well as the following standards:

(I) identify and quantify causes and effects of uncertainties in measured data;
(J) organize and evaluate data and make inferences from data, including the use of tables, charts, and graphs.

Section Key Terms

[OL] Pre-assessment for this section could involve asking students what experience they have had with the four fundamental units in their daily lives. One could also poll the class for what they think accuracy, precision, and uncertainty refer to. For graphing, students could make a quick graph of some data and then edit their graph after reading to note ways they could improve the clarity of their graph.

The Role of Units

Physicists, like other scientists, make observations and ask basic questions. For example, how big is an object? How much mass does it have? How far did it travel? To answer these questions, they make measurements with various instruments (e.g., meter stick, balance, stopwatch, etc.).

The measurements of physical quantities are expressed in terms of units, which are standardized values. For example, the length of a race, which is a physical quantity, can be expressed in meters (for sprinters) or kilometers (for long distance runners). Without standardized units, it would be extremely difficult for scientists to express and compare measured values in a meaningful way ( Figure 1.13 ).

All physical quantities in the International System of Units (SI) are expressed in terms of combinations of seven fundamental physical units, which are units for: length, mass, time, electric current, temperature, amount of a substance, and luminous intensity.

SI Units: Fundamental and Derived Units

In any system of units, the units for some physical quantities must be defined through a measurement process. These are called the base quantities for that system and their units are the system’s base units . All other physical quantities can then be expressed as algebraic combinations of the base quantities. Each of these physical quantities is then known as a derived quantity and each unit is called a derived unit . The choice of base quantities is somewhat arbitrary, as long as they are independent of each other and all other quantities can be derived from them. Typically, the goal is to choose physical quantities that can be measured accurately to a high precision as the base quantities. The reason for this is simple. Since the derived units can be expressed as algebraic combinations of the base units, they can only be as accurate and precise as the base units from which they are derived.

[OL] As a clarification, certain countries use the British system for a few of their measurements. For example, Britain still uses the pint to measure beer, miles to measure road distances, and pounds to measure body weight (although weight must be reported in kg in British medical records). The British people still use the British system extensively in their everyday lives, but the metric system is the official standard for the government. Likewise, many oil-producing countries measure oil in British gallons.

Based on such considerations, the International Standards Organization recommends using seven base quantities, which form the International System of Quantities (ISQ). These are the base quantities used to define the SI base units. ( Table 1.1 ) lists these seven ISQ base quantities and the corresponding SI base units.

The SI unit for length is the meter (m). The definition of the meter has changed over time to become more accurate and precise. The meter was first defined in 1791 as 1/10,000,000 of the distance from the equator to the North Pole. This measurement was improved in 1889 by redefining the meter to be the distance between two engraved lines on a platinum-iridium bar. (The bar is now housed at the International Bureau of Weights and Measures, near Paris). By 1960, some distances could be measured more precisely by comparing them to wavelengths of light. The meter was redefined as 1,650,763.73 wavelengths of orange light emitted by krypton atoms. In 1983, the meter was given its present definition as the distance light travels in a vacuum in 1/ 299,792,458 of a second ( Figure 1.14 ).

The Kilogram

The SI unit for mass is the kilogram (abbreviated kg); it was previously defined to be the mass of a platinum-iridium cylinder kept with the old meter standard at the International Bureau of Weights and Measures near Paris. Exact replicas of the previously defined kilogram are also kept at the United States’ National Institute of Standards and Technology, or NIST, located in Gaithersburg, Maryland outside of Washington D.C., and at other locations around the world. The determination of all other masses could be ultimately traced to a comparison with the standard mass. Even though the platinum-iridium cylinder was resistant to corrosion, airborne contaminants were able to adhere to its surface, slightly changing its mass over time. In May 2019, the scientific community adopted a more stable definition of the kilogram. The kilogram is now defined in terms of the second, the meter, and Planck's constant, h (a quantum mechanical value that relates a photon's energy to its frequency).

The SI unit for time, the second (s) also has a long history. For many years it was defined as 1/86,400 of an average solar day. However, the average solar day is actually very gradually getting longer due to gradual slowing of Earth’s rotation. Accuracy in the fundamental units is essential, since all other measurements are derived from them. Therefore, a new standard was adopted to define the second in terms of a non-varying, or constant, physical phenomenon. One constant phenomenon is the very steady vibration of Cesium atoms, which can be observed and counted. This vibration forms the basis of the cesium atomic clock . In 1967, the second was redefined as the time required for 9,192,631,770 Cesium atom vibrations ( Figure 1.15 ).

[BL] An average solar day was used to originally define the second because the length of a solar day varies throughout the year due to Earth’s tilt of its axis as well as its elliptical orbit. The accumulation of these variations could result in a day length difference of up to 16 minutes during different seasons. Using an average solar day resolves these variations in day length.

Electric current is measured in the ampere (A), named after Andre Ampere. You have probably heard of amperes, or amps , when people discuss electrical currents or electrical devices. Understanding an ampere requires a basic understanding of electricity and magnetism, something that will be explored in depth in later chapters of this book. Basically, two parallel wires with an electric current running through them will produce an attractive force on each other. One ampere is defined as the amount of electric current that will produce an attractive force of 2.7 × × 10 –7 newton per meter of separation between the two wires (the newton is the derived unit of force).

[BL] Some students may not know that a vacuum is a region of space that contains no air.

The SI unit of temperature is the kelvin (or kelvins, but not degrees kelvin). This scale is named after physicist William Thomson, Lord Kelvin, who was the first to call for an absolute temperature scale. The Kelvin scale is based on absolute zero. This is the point at which all thermal energy has been removed from all atoms or molecules in a system. This temperature, 0 K, is equal to −273.15 °C and −459.67 °F. Conveniently, the Kelvin scale actually changes in the same way as the Celsius scale. For example, the freezing point (0 °C) and boiling points of water (100 °C) are 100 degrees apart on the Celsius scale. These two temperatures are also 100 kelvins apart (freezing point = 273.15 K; boiling point = 373.15 K).

Metric Prefixes

Physical objects or phenomena may vary widely. For example, the size of objects varies from something very small (like an atom) to something very large (like a star). Yet the standard metric unit of length is the meter. So, the metric system includes many prefixes that can be attached to a unit. Each prefix is based on factors of 10 (10, 100, 1,000, etc., as well as 0.1, 0.01, 0.001, etc.). Table 1.2 gives the metric prefixes and symbols used to denote the different various factors of 10 in the metric system.

The metric system is convenient because conversions between metric units can be done simply by moving the decimal place of a number. This is because the metric prefixes are sequential powers of 10. There are 100 centimeters in a meter, 1000 meters in a kilometer, and so on. In nonmetric systems, such as U.S. customary units , the relationships are less simple—there are 12 inches in a foot, 5,280 feet in a mile, 4 quarts in a gallon, and so on. Another advantage of the metric system is that the same unit can be used over extremely large ranges of values simply by switching to the most-appropriate metric prefix. For example, distances in meters are suitable for building construction, but kilometers are used to describe road construction. Therefore, with the metric system, there is no need to invent new units when measuring very small or very large objects—you just have to move the decimal point (and use the appropriate prefix).

Known Ranges of Length, Mass, and Time

Table 1.3 lists known lengths, masses, and time measurements. You can see that scientists use a range of measurement units. This wide range demonstrates the vastness and complexity of the universe, as well as the breadth of phenomena physicists study. As you examine this table, note how the metric system allows us to discuss and compare an enormous range of phenomena, using one system of measurement ( Figure 1.16 and Figure 1.17 ).

Using Scientific Notation with Physical Measurements

Scientific notation is a way of writing numbers that are too large or small to be conveniently written as a decimal. For example, consider the number 840,000,000,000,000. It’s a rather large number to write out. The scientific notation for this number is 8.40 × × 10 14 . Scientific notation follows this general format

In this format x is the value of the measurement with all placeholder zeros removed. In the example above, x is 8.4. The x is multiplied by a factor, 10 y , which indicates the number of placeholder zeros in the measurement. Placeholder zeros are those at the end of a number that is 10 or greater, and at the beginning of a decimal number that is less than 1. In the example above, the factor is 10 14 . This tells you that you should move the decimal point 14 positions to the right, filling in placeholder zeros as you go. In this case, moving the decimal point 14 places creates only 13 placeholder zeros, indicating that the actual measurement value is 840,000,000,000,000.

Numbers that are fractions can be indicated by scientific notation as well. Consider the number 0.0000045. Its scientific notation is 4.5 × × 10 –6 . Its scientific notation has the same format

Here, x is 4.5. However, the value of y in the 10 y factor is negative, which indicates that the measurement is a fraction of 1. Therefore, we move the decimal place to the left, for a negative y . In our example of 4.5 × × 10 –6 , the decimal point would be moved to the left six times to yield the original number, which would be 0.0000045.

The term order of magnitude refers to the power of 10 when numbers are expressed in scientific notation. Quantities that have the same power of 10 when expressed in scientific notation, or come close to it, are said to be of the same order of magnitude. For example, the number 800 can be written as 8 × × 10 2 , and the number 450 can be written as 4.5 × × 10 2 . Both numbers have the same value for y . Therefore, 800 and 450 are of the same order of magnitude. Similarly, 101 and 99 would be regarded as the same order of magnitude, 10 2 . Order of magnitude can be thought of as a ballpark estimate for the scale of a value. The diameter of an atom is on the order of 10 −9 m, while the diameter of the sun is on the order of 10 9 m. These two values are 18 orders of magnitude apart.

Scientists make frequent use of scientific notation because of the vast range of physical measurements possible in the universe, such as the distance from Earth to the moon ( Figure 1.18 ), or to the nearest star.

Unit Conversion and Dimensional Analysis

It is often necessary to convert from one type of unit to another. For example, if you are reading a European cookbook in the United States, some quantities may be expressed in liters and you need to convert them to cups. A Canadian tourist driving through the United States might want to convert miles to kilometers, to have a sense of how far away his next destination is. A doctor in the United States might convert a patient’s weight in pounds to kilograms.

Let’s consider a simple example of how to convert units within the metric system. How can we convert 1 hour to seconds?

First, we need to determine a conversion factor. A conversion factor is a ratio expressing how many of one unit are equal to another unit. A conversion factor is simply a fraction which equals 1. You can multiply any number by 1 and get the same value. When you multiply a number by a conversion factor, you are simply multiplying it by one. For example, the following are conversion factors: (1 foot)/(12 inches) = 1 to convert inches to feet, (1 meter)/(100 centimeters) = 1 to convert centimeters to meters, (1 minute)/(60 seconds) = 1 to convert seconds to minutes.

Now we can set up our unit conversion. We will write the units that we have and then multiply them by the conversion factor (1 km/1,000m) = 1, so we are simply multiplying 80m by 1:

When there is a unit in the original number, and a unit in the denominator (bottom) of the conversion factor, the units cancel. In this case, hours and minutes cancel and the value in seconds remains.

You can use this method to convert between any types of unit, including between the U.S. customary system and metric system. Notice also that, although you can multiply and divide units algebraically, you cannot add or subtract different units. An expression like 10 km + 5 kg makes no sense. Even adding two lengths in different units, such as 10 km + 20 m does not make sense. You express both lengths in the same unit. See Reference Tables for a more complete list of conversion factors.

Worked Example

Unit conversions: a short drive home.

Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and (b) in meters per second (m/s). (Note—Average speed is distance traveled divided by time of travel.)

First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.

Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now—average speed and other motion concepts will be covered in a later module.) In equation form,

Substitute the given values for distance and time.

Convert km/min to km/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is 60 min/1 h 60 min/1 h . Thus,

To check your answer, consider the following:

Be sure that you have properly cancelled the units in the unit conversion. If you have written the unit conversion factor upside down, the units will not cancel properly in the equation. If you accidentally get the ratio upside down, then the units will not cancel; rather, they will give you the wrong units as follows

which are obviously not the desired units of km/h.

Check that the units of the final answer are the desired units. The problem asked us to solve for average speed in units of km/h and we have indeed obtained these units.
Check the significant figures. Because each of the values given in the problem has three significant figures, the answer should also have three significant figures. The answer 30.0 km/h does indeed have three significant figures, so this is appropriate. Note that the significant figures in the conversion factor are not relevant because an hour is defined to be 60 min, so the precision of the conversion factor is perfect.
Next, check whether the answer is reasonable. Let us consider some information from the problem—if you travel 10 km in a third of an hour (20 min), you would travel three times that far in an hour. The answer does seem reasonable.

There are several ways to convert the average speed into meters per second.

Start with the answer to (a) and convert km/h to m/s. Two conversion factors are needed—one to convert hours to seconds, and another to convert kilometers to meters.

Multiplying by these yields

If we had started with 0.500 km/min, we would have needed different conversion factors, but the answer would have been the same: 8.33 m/s.

You may have noted that the answers in the worked example just covered were given to three digits. Why? When do you need to be concerned about the number of digits in something you calculate? Why not write down all the digits your calculator produces?

Using Physics to Evaluate Promotional Materials

A commemorative coin that is 2″ in diameter is advertised to be plated with 15 mg of gold. If the density of gold is 19.3 g/cc, and the amount of gold around the edge of the coin can be ignored, what is the thickness of the gold on the top and bottom faces of the coin?

To solve this problem, the volume of the gold needs to be determined using the gold’s mass and density. Half of that volume is distributed on each face of the coin, and, for each face, the gold can be represented as a cylinder that is 2″ in diameter with a height equal to the thickness. Use the volume formula for a cylinder to determine the thickness.

The mass of the gold is given by the formula m = ρ V = 15 × 10 − 3 g, m = ρ V = 15 × 10 − 3 g, where ρ = 19.3 g/cc ρ = 19.3 g/cc and V is the volume. Solving for the volume gives V = m ρ = 15 × 10 − 3 g 19.3 g/cc ≅ 7.8 × 10 − 4 cc. V = m ρ = 15 × 10 − 3 g 19.3 g/cc ≅ 7.8 × 10 − 4 cc.

If t is the thickness, the volume corresponding to half the gold is 1 2 ( 7.8 × 10 − 4 ) = π r 2 t = π ( 2.54 ) 2 t, 1 2 ( 7.8 × 10 − 4 ) = π r 2 t = π ( 2.54 ) 2 t, where the 1″ radius has been converted to cm. Solving for the thickness gives t = ( 3.9 × 10 − 4 ) π ( 2.54 ) 2 ≅ 1.9 × 10 − 5 cm = 0.00019 mm. t = ( 3.9 × 10 − 4 ) π ( 2.54 ) 2 ≅ 1.9 × 10 − 5 cm = 0.00019 mm.

The amount of gold used is stated to be 15 mg, which is equivalent to a thickness of about 0.00019 mm. The mass figure may make the amount of gold sound larger, both because the number is much bigger (15 versus 0.00019), and because people may have a more intuitive feel for how much a millimeter is than for how much a milligram is. A simple analysis of this sort can clarify the significance of claims made by advertisers.

Ask students to find other promotional materials that make claims that can be analyzed using physics principles. Compile any items that come in for later use at appropriate points in the course. For example, after covering power consumption in electric circuits, compare the performance of electric fireplaces advertised as revolutionary to the performance of standard space heaters.

Accuracy, Precision and Significant Figures

Science is based on experimentation that requires good measurements. The validity of a measurement can be described in terms of its accuracy and its precision (see Figure 1.19 and Figure 1.20 ). Accuracy is how close a measurement is to the correct value for that measurement. For example, let us say that you are measuring the length of standard piece of printer paper. The packaging in which you purchased the paper states that it is 11 inches long, and suppose this stated value is correct. You measure the length of the paper three times and obtain the following measurements: 11.1 inches, 11.2 inches, and 10.9 inches. These measurements are quite accurate because they are very close to the correct value of 11.0 inches. In contrast, if you had obtained a measurement of 12 inches, your measurement would not be very accurate. This is why measuring instruments are calibrated based on a known measurement. If the instrument consistently returns the correct value of the known measurement, it is safe for use in finding unknown values.

Precision states how well repeated measurements of something generate the same or similar results. Therefore, the precision of measurements refers to how close together the measurements are when you measure the same thing several times. One way to analyze the precision of measurements would be to determine the range, or difference between the lowest and the highest measured values. In the case of the printer paper measurements, the lowest value was 10.9 inches and the highest value was 11.2 inches. Thus, the measured values deviated from each other by, at most, 0.3 inches. These measurements were reasonably precise because they varied by only a fraction of an inch. However, if the measured values had been 10.9 inches, 11.1 inches, and 11.9 inches, then the measurements would not be very precise because there is a lot of variation from one measurement to another.

The measurements in the paper example are both accurate and precise, but in some cases, measurements are accurate but not precise, or they are precise but not accurate. Let us consider a GPS system that is attempting to locate the position of a restaurant in a city. Think of the restaurant location as existing at the center of a bull’s-eye target. Then think of each GPS attempt to locate the restaurant as a black dot on the bull’s eye.

In Figure 1.21 , you can see that the GPS measurements are spread far apart from each other, but they are all relatively close to the actual location of the restaurant at the center of the target. This indicates a low precision, high accuracy measuring system. However, in Figure 1.22 , the GPS measurements are concentrated quite closely to one another, but they are far away from the target location. This indicates a high precision, low accuracy measuring system. Finally, in Figure 1.23 , the GPS is both precise and accurate, allowing the restaurant to be located.

Uncertainty

The accuracy and precision of a measuring system determine the uncertainty of its measurements. Uncertainty is a way to describe your confidence in your measured value, or the range of values that would be consistent with the data. If your measurements are not very accurate or precise, then the uncertainty of your values will be very high. In more general terms, uncertainty can be thought of as a disclaimer for your measured values. For example, if someone asked you to provide the mileage on your car, you might say that it is 45,000 miles, plus or minus 500 miles. The plus or minus amount is the uncertainty in your value. That is, you are indicating that the actual mileage of your car might be as low as 44,500 miles or as high as 45,500 miles, or anywhere in between. All measurements contain some amount of uncertainty. In our example of measuring the length of the paper, we might say that the length of the paper is 11 inches plus or minus 0.2 inches or 11.0 ± 0.2 inches. The uncertainty in a measurement, A , is often denoted as δA ("delta A "). The actual value of the object may not be within the range given by the measurement and its uncertainty. In our paper length example above, a new set of measurements might produce a length of 14.0 ± 0.2 inches, with the uncertainty based on the accuracy or our reading or repeated measurements. We would also, however, conclude that either one of our measurement sets is incorrect due to an offset in the measurement process in that set, or our measurement correctly identifies that we are measuring different papers. In the former case, the discrepancy between the measured value and the actual value is called a systematic error.

The factors contributing to uncertainty in a measurement include the following:

Limitations of the measuring device
The skill of the person making the measurement
Irregularities in the object being measured
Any other factors that affect the outcome (highly dependent on the situation)

In the printer paper example uncertainty could be caused by: the fact that the smallest division on the ruler is 0.1 inches, the person using the ruler has bad eyesight, or uncertainty caused by the paper cutting machine (e.g., one side of the paper is slightly longer than the other.) It is good practice to carefully consider all possible sources of uncertainty in a measurement and reduce or eliminate them.

Percent Uncertainty

One method of expressing uncertainty is as a percent of the measured value. If a measurement, A , is expressed with uncertainty, δ A , the percent uncertainty is

Calculating Percent Uncertainty: A Bag of Apples

A grocery store sells 5-lb bags of apples. You purchase four bags over the course of a month and weigh the apples each time. You obtain the following measurements:

Week 1 weight: 4.8 lb 4.8 lb
Week 2 weight: 5.3 lb 5.3 lb
Week 3 weight: 4.9 lb 4.9 lb
Week 4 weight: 5.4 lb 5.4 lb

You determine that the expected weight of a 5 lb bag has an uncertainty of ±0.4 lb. What is the percent uncertainty of the bag’s weight?

First, observe that the expected value of the bag’s weight, A A , is 5 lb. The uncertainty in this value, δ A δ A , is 0.4 lb. We can use the following equation to determine the percent uncertainty of the weight

Plug the known values into the equation

We can conclude that the weight of the apple bag is 5 lb ± 8 percent. Consider how this percent uncertainty would change if the bag of apples were half as heavy, but the uncertainty in the weight remained the same. Hint for future calculations: when calculating percent uncertainty, always remember that you must multiply the fraction by 100 percent. If you do not do this, you will have a decimal quantity, not a percent value.

Uncertainty in Calculations

There is an uncertainty in anything calculated from measured quantities. For example, the area of a floor calculated from measurements of its length and width has an uncertainty because the both the length and width have uncertainties. How big is the uncertainty in something you calculate by multiplication or division? If the measurements in the calculation have small uncertainties (a few percent or less), then the method of adding percents can be used. This method says that the percent uncertainty in a quantity calculated by multiplication or division is the sum of the percent uncertainties in the items used to make the calculation. For example, if a floor has a length of 4.00 m and a width of 3.00 m, with uncertainties of 2 percent and 1 percent, respectively, then the area of the floor is 12.0 m 2 and has an uncertainty of 3 percent (expressed as an area this is 0.36 m 2 , which we round to 0.4 m 2 since the area of the floor is given to a tenth of a square meter).

For more information on the accuracy, precision, and uncertainty of measurements based upon the units of measurement, visit this website .

Precision of Measuring Tools and Significant Figures

An important factor in the accuracy and precision of measurements is the precision of the measuring tool. In general, a precise measuring tool is one that can measure values in very small increments. For example, consider measuring the thickness of a coin. A standard ruler can measure thickness to the nearest millimeter, while a micrometer can measure the thickness to the nearest 0.005 millimeter. The micrometer is a more precise measuring tool because it can measure extremely small differences in thickness. The more precise the measuring tool, the more precise and accurate the measurements can be.

When we express measured values, we can only list as many digits as we initially measured with our measuring tool (such as the rulers shown in Figure 1.24 ). For example, if you use a standard ruler to measure the length of a stick, you may measure it with a decimeter ruler as 3.6 cm. You could not express this value as 3.65 cm because your measuring tool was not precise enough to measure a hundredth of a centimeter. It should be noted that the last digit in a measured value has been estimated in some way by the person performing the measurement. For example, the person measuring the length of a stick with a ruler notices that the stick length seems to be somewhere in between 36 mm and 37 mm. He or she must estimate the value of the last digit. The rule is that the last digit written down in a measurement is the first digit with some uncertainty. For example, the last measured value 36.5 mm has three digits, or three significant figures. The number of significant figures in a measurement indicates the precision of the measuring tool. The more precise a measuring tool is, the greater the number of significant figures it can report.

Special consideration is given to zeros when counting significant figures. For example, the zeros in 0.053 are not significant because they are only placeholders that locate the decimal point. There are two significant figures in 0.053—the 5 and the 3. However, if the zero occurs between other significant figures, the zeros are significant. For example, both zeros in 10.053 are significant, as these zeros were actually measured. Therefore, the 10.053 placeholder has five significant figures. The zeros in 1300 may or may not be significant, depending on the style of writing numbers. They could mean the number is known to the last zero, or the zeros could be placeholders. So 1300 could have two, three, or four significant figures. To avoid this ambiguity, write 1300 in scientific notation as 1.3 × 10 3 . Only significant figures are given in the x factor for a number in scientific notation (in the form x × 10 y x × 10 y ). Therefore, we know that 1 and 3 are the only significant digits in this number. In summary, zeros are significant except when they serve only as placeholders. Table 1.4 provides examples of the number of significant figures in various numbers.

Significant Figures in Calculations

When combining measurements with different degrees of accuracy and precision, the number of significant digits in the final answer can be no greater than the number of significant digits in the least precise measured value. There are two different rules, one for multiplication and division and another rule for addition and subtraction, as discussed below.

For multiplication and division: The answer should have the same number of significant figures as the starting value with the fewest significant figures. For example, the area of a circle can be calculated from its radius using A = π r 2 A = π r 2 . Let us see how many significant figures the area will have if the radius has only two significant figures, for example, r = 2.0 m. Then, using a calculator that keeps eight significant figures, you would get

But because the radius has only two significant figures, the area calculated is meaningful only to two significant figures or

even though the value of π π is meaningful to at least eight digits.

For addition and subtraction : The answer should have the same number places (e.g. tens place, ones place, tenths place, etc.) as the least-precise starting value. Suppose that you buy 7.56 kg of potatoes in a grocery store as measured with a scale having a precision of 0.01 kg. Then you drop off 6.052 kg of potatoes at your laboratory as measured by a scale with a precision of 0.001 kg. Finally, you go home and add 13.7 kg of potatoes as measured by a bathroom scale with a precision of 0.1 kg. How many kilograms of potatoes do you now have, and how many significant figures are appropriate in the answer? The mass is found by simple addition and subtraction:

The least precise measurement is 13.7 kg. This measurement is expressed to the 0.1 decimal place, so our final answer must also be expressed to the 0.1 decimal place. Thus, the answer should be rounded to the tenths place, giving 15.2 kg. The same is true for non-decimal numbers. For example,

We cannot report the decimal places in the answer because 2 has no decimal places that would be significant. Therefore, we can only report to the ones place.

It is a good idea to keep extra significant figures while calculating, and to round off to the correct number of significant figures only in the final answers. The reason is that small errors from rounding while calculating can sometimes produce significant errors in the final answer. As an example, try calculating 5,098 − ( 5.000 ) × ( 1,010 ) 5,098 − ( 5.000 ) × ( 1,010 ) to obtain a final answer to only two significant figures. Keeping all significant during the calculation gives 48. Rounding to two significant figures in the middle of the calculation changes it to 5,100 – (5 .000) × (1,000) = 100, 5,100 – (5 .000) × (1,000) = 100, which is way off. You would similarly avoid rounding in the middle of the calculation in counting and in doing accounting, where many small numbers need to be added and subtracted accurately to give possibly much larger final numbers.

Remind students that they will be expected to report the proper number of significant figures on assignment and test problems.

Significant Figures in this Text

In this textbook, most numbers are assumed to have three significant figures. Furthermore, consistent numbers of significant figures are used in all worked examples. You will note that an answer given to three digits is based on input good to at least three digits. If the input has fewer significant figures, the answer will also have fewer significant figures. Care is also taken that the number of significant figures is reasonable for the situation posed. In some topics, such as optics, more than three significant figures will be used. Finally, if a number is exact, such as the 2 in the formula, c = 2 π r c = 2 π r , it does not affect the number of significant figures in a calculation.

Approximating Vast Numbers: a Trillion Dollars

The U.S. federal deficit in the 2008 fiscal year was a little greater than $10 trillion. Most of us do not have any concept of how much even one trillion actually is. Suppose that you were given a trillion dollars in $100 bills. If you made 100-bill stacks, like that shown in Figure 1.25 , and used them to evenly cover a football field (between the end zones), make an approximation of how high the money pile would become. (We will use feet/inches rather than meters here because football fields are measured in yards.) One of your friends says 3 in., while another says 10 ft. What do you think?

When you imagine the situation, you probably envision thousands of small stacks of 100 wrapped $100 bills, such as you might see in movies or at a bank. Since this is an easy-to-approximate quantity, let us start there. We can find the volume of a stack of 100 bills, find out how many stacks make up one trillion dollars, and then set this volume equal to the area of the football field multiplied by the unknown height.

Calculate the volume of a stack of 100 bills. The dimensions of a single bill are approximately 3 in. by 6 in. A stack of 100 of these is about 0.5 in. thick. So the total volume of a stack of 100 bills is volume of stack = length × width × height, volume of stack = 6 in . × 3 in . × 0 .5 in ., volume of stack = 9 in . 3 . volume of stack = length × width × height, volume of stack = 6 in . × 3 in . × 0 .5 in ., volume of stack = 9 in . 3 .

Calculate the number of stacks. Note that a trillion dollars is equal to $ 1 × 10 12 $ 1 × 10 12 , and a stack of one-hundred $ 100 $ 100 bills is equal to $ 10 , 000 , $ 10 , 000 , or $ 1 × 10 4 $ 1 × 10 4 . The number of stacks you will have is

Calculate the area of a football field in square inches. The area of a football field is 100 yd × 50 yd 100 yd × 50 yd , which gives 5 , 000 yd 2 5 , 000 yd 2 . Because we are working in inches, we need to convert square yards to square inches

This conversion gives us 6 × 10 6 in . 2 6 × 10 6 in . 2 for the area of the field. (Note that we are using only one significant figure in these calculations.)

Calculate the total volume of the bills. The volume of all the $100-bill stacks is 9 in . 3 / stack × 10 8 stacks = 9 × 10 8 in . 3 9 in . 3 / stack × 10 8 stacks = 9 × 10 8 in . 3

The height of the money will be about 100 in. high. Converting this value to feet gives

The final approximate value is much higher than the early estimate of 3 in., but the other early estimate of 10 ft (120 in.) was roughly correct. How did the approximation measure up to your first guess? What can this exercise tell you in terms of rough guesstimates versus carefully calculated approximations?

In the example above, the final approximate value is much higher than the first friend’s early estimate of 3 in. However, the other friend’s early estimate of 10 ft. (120 in.) was roughly correct. How did the approximation measure up to your first guess? What can this exercise suggest about the value of rough guesstimates versus carefully calculated approximations?

In [link] , point out to students the importance of precision in their measurements. Greater precision allows measurements to be less uncertain, and therefore, a close approximation rather than a guesstimate.

Graphing in Physics

Most results in science are presented in scientific journal articles using graphs. Graphs present data in a way that is easy to visualize for humans in general, especially someone unfamiliar with what is being studied. They are also useful for presenting large amounts of data or data with complicated trends in an easily-readable way.

One commonly-used graph in physics and other sciences is the line graph , probably because it is the best graph for showing how one quantity changes in response to the other. Let’s build a line graph based on the data in Table 1.5 , which shows the measured distance that a train travels from its station versus time. Our two variables , or things that change along the graph, are time in minutes, and distance from the station, in kilometers. Remember that measured data may not have perfect accuracy.

Draw the two axes. The horizontal axis, or x -axis, shows the independent variable , which is the variable that is controlled or manipulated. The vertical axis, or y -axis, shows the dependent variable , the non-manipulated variable that changes with (or is dependent on) the value of the independent variable. In the data above, time is the independent variable and should be plotted on the x -axis. Distance from the station is the dependent variable and should be plotted on the y -axis.
Label each axes on the graph with the name of each variable, followed by the symbol for its units in parentheses. Be sure to leave room so that you can number each axis. In this example, use Time (min) as the label for the x -axis.

Next, you must determine the best scale to use for numbering each axis. Because the time values on the x -axis are taken every 10 minutes, we could easily number the x -axis from 0 to 70 minutes with a tick mark every 10 minutes. Likewise, the y -axis scale should start low enough and continue high enough to include all of the distance from station values. A scale from 0 km to 160 km should suffice, perhaps with a tick mark every 10 km.

In general, you want to pick a scale for both axes that 1) shows all of your data, and 2) makes it easy to identify trends in your data. If you make your scale too large, it will be harder to see how your data change. Likewise, the smaller and more fine you make your scale, the more space you will need to make the graph. The number of significant figures in the axis values should be coarser than the number of significant figures in the measurements.

Add a title to the top of the graph to state what the graph is describing, such as the y -axis parameter vs. the x -axis parameter. In the graph shown here, the title is train motion . It could also be titled distance of the train from the station vs. time.

[OL] The importance of bar graphs should also be mentioned as a useful way to show data relations when one variable is not continuous, such as in a frequency histogram, which compares how many data points fall into discrete categories.

[OL] If students have difficulty understanding the difference between dependent and independent variables in the train example, explain that time is independent because it will continue to move forward at the same rate whether the train leaves the station or not.

Analyzing a Graph Using Its Equation

One way to get a quick snapshot of a dataset is to look at the equation of its trend line . If the graph produces a straight line, the equation of the trend line takes the form

The b in the equation is the y -intercept while the m in the equation is the slope . The y -intercept tells you at what y value the line intersects the y -axis. In the case of the graph above, the y -intercept occurs at 0, at the very beginning of the graph. The y -intercept, therefore, lets you know immediately where on the y -axis the plot line begins.

The m in the equation is the slope. This value describes how much the line on the graph moves up or down on the y -axis along the line’s length. The slope is found using the following equation

In order to solve this equation, you need to pick two points on the line (preferably far apart on the line so the slope you calculate describes the line accurately). The quantities Y 2 and Y 1 represent the y -values from the two points on the line (not data points) that you picked, while X 2 and X 1 represent the two x -values of the those points.

What can the slope value tell you about the graph? The slope of a perfectly horizontal line will equal zero, while the slope of a perfectly vertical line will be undefined because you cannot divide by zero. A positive slope indicates that the line moves up the y -axis as the x -value increases while a negative slope means that the line moves down the y -axis. The more negative or positive the slope is, the steeper the line moves up or down, respectively. The slope of our graph in Figure 1.26 is calculated below based on the two endpoints of the line

Equation of line: y = ( 2.0 km/min ) x + 0 y = ( 2.0 km/min ) x + 0

Because the x axis is time in minutes, we would actually be more likely to use the time t as the independent ( x- axis) variable and write the equation as

The formula y = m x + b y = m x + b only applies to linear relationships , or ones that produce a straight line. Another common type of line in physics is the quadratic relationship , which occurs when one of the variables is squared. One quadratic relationship in physics is the relation between the speed of an object its centripetal acceleration, which is used to determine the force needed to keep an object moving in a circle. Another common relationship in physics is the inverse relationship , in which one variable decreases whenever the other variable increases. An example in physics is Coulomb’s law. As the distance between two charged objects increases, the electrical force between the two charged objects decreases. Inverse proportionality , such the relation between x and y in the equation

for some number k , is one particular kind of inverse relationship. A third commonly-seen relationship is the exponential relationship , in which a change in the independent variable produces a proportional change in the dependent variable. As the value of the dependent variable gets larger, its rate of growth also increases. For example, bacteria often reproduce at an exponential rate when grown under ideal conditions. As each generation passes, there are more and more bacteria to reproduce. As a result, the growth rate of the bacterial population increases every generation ( Figure 1.28 ).

Using Logarithmic Scales in Graphing

Sometimes a variable can have a very large range of values. This presents a problem when you’re trying to figure out the best scale to use for your graph’s axes. One option is to use a logarithmic (log) scale . In a logarithmic scale, the value each mark labels is the previous mark’s value multiplied by some constant. For a log base 10 scale, each mark labels a value that is 10 times the value of the mark before it. Therefore, a base 10 logarithmic scale would be numbered: 0, 10, 100, 1,000, etc. You can see how the logarithmic scale covers a much larger range of values than the corresponding linear scale, in which the marks would label the values 0, 10, 20, 30, and so on.

If you use a logarithmic scale on one axis of the graph and a linear scale on the other axis, you are using a semi-log plot . The Richter scale, which measures the strength of earthquakes, uses a semi-log plot. The degree of ground movement is plotted on a logarithmic scale against the assigned intensity level of the earthquake, which ranges linearly from 1-10 ( Figure 1.29 (a) ).

If a graph has both axes in a logarithmic scale, then it is referred to as a log-log plot . The relationship between the wavelength and frequency of electromagnetic radiation such as light is usually shown as a log-log plot ( Figure 1.29 (b) ). Log-log plots are also commonly used to describe exponential functions, such as radioactive decay.

Method of Adding Percents: Shingling Your Roof

A series of shingles are used to protect the roof of a home. Using a measuring tape, you measure one shingle and find its dimensions to be 44 cm by 100 cm. Knowing that your measurements are not perfect, you estimate an uncertainty of ±0.5 cm. Following the method of adding percents, what is the area of the shingle, including uncertainty?

While calculating the area of the shingle is straightforward (44 cm x 100 cm = 4400 cm 2 ), determining the percent uncertainty is more challenging. In order to use the method of adding percents, you must first calculate the percent uncertainty of each measurement.

Length % Uncertainty: 𝜹A/A x 100% = 0.5/44 x 100% = 1.1% Width % Uncertainty: 𝜹A/A x 100% = 0.5/100 x 100% = 0.5%

Adding Percents: 1.1% + 0.5% = 1.6% uncertainty

Area of the Shingle: 4400 cm 2 ± 1.6%

Note that this uncertainty can also be expressed in metric terms.

1.6% x 4400 cm 2 = 70.4 cm 2

Area of the Shingle: 4400 ± 70.4 cm 2

Knowing the percent uncertainty of a shingle can help a contractor determine the number of shingles needed, and therefore the cost, of roofing a new home. Consider how using smaller shingles would affect this uncertainty, and what role this would play in the cost estimation process.

Virtual Physics

Graphing lines.

In this simulation you will examine how changing the slope and y -intercept of an equation changes the appearance of a plotted line. Select slope-intercept form and drag the blue circles along the line to change the line’s characteristics. Then, play the line game and see if you can determine the slope or y -intercept of a given line.

Grasp Check

How would the following changes affect a line that is neither horizontal nor vertical and has a positive slope?

increase the slope but keeping the y -intercept constant
Increasing the slope will cause the line to rotate clockwise around the y -intercept. Increasing the y -intercept will cause the line to move vertically up on the graph without changing the line’s slope.
Increasing the slope will cause the line to rotate counter-clockwise around the y -intercept. Increasing the y -intercept will cause the line to move vertically up on the graph without changing the line’s slope.
Increasing the slope will cause the line to rotate clockwise around the y -intercept. Increasing the y -intercept will cause the line to move horizontally right on the graph without changing the line’s slope.
Increasing the slope will cause the line to rotate counter-clockwise around the y -intercept. Increasing the y -intercept will cause the line to move horizontally right on the graph without changing the line’s slope.

Check Your Understanding

Conversion between units is easier in metric units.
Comparison of physical quantities is easy in metric units.
Metric units are more modern than English units.
Metric units are based on powers of 2.
Precision states how much repeated measurements generate the same or closely similar results, while accuracy states how close a measurement is to the true value of the measurement.
Precision states how close a measurement is to the true value of the measurement, while accuracy states how much repeated measurements generate the same or closely similar result.
Precision and accuracy are the same thing. They state how much repeated measurements generate the same or closely similar results.
Precision and accuracy are the same thing. They state how close a measurement is to the true value of the measurement.

Use the Check Your Understanding questions to assess students’ achievement of the sections learning objectives. If students are struggling with a specific objective, the Check Your Understanding will help identify which and direct students to the relevant content.

1 See Appendix A for a discussion of powers of 10.

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Paper Quantities – Ream, Quire, Bundle, Bale & Pallet

Post author: Alan Lee
Post category: Paper Weights
Post last modified: July 15, 2023
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Have you ever heard about Paper Quantities such as Ream, Quire? We all use Paper for a wide range of purposes. Letters, Documents, Envelopes, Cards, Invitations, Posters, and so on. This wide range of usage has led to the Standardization of Paper into different sizes and types, into different categories, depending on uses, the dimensions and also the weight. Paper is generally sold out to the services in reams or quires and commercially in bundles, bales, and pallets. Paper quantities have faced numerous changes. In new periods the heap has improved, patterned at 500 sheets. And the bundle of related documents at 25 sheets.

But, Paper cannot be directly made into these Standard Sizes. First, the paper is made as large sheets of unfathomable dimensions and sizes in Paper Mills from wood pulp and other substances. Later, these big sheets are cut into smaller dimensions according to need or according to the Standards. These sized papers further undergo process and size checks to ensure the following things:

The paper is a rectangle. That is, all corners are precisely 90 degrees.
The paper is of the dimensions as defined by the Standards and the error is within the Tolerance limits mentioned.
The thickness of the paper is well enough to make it durable.
The cuts are well made to not leave excess papers, or remnant edges onto the sized paper.

This is legendary as the total load and is ordinarily provided in pounds (lbs). The essential heaviness is the thickness of a 500-page heap of complete paper (except Reams & Quires – Paper Quantities explained for more confidential information on the heap).

Overview of Ream, Quire, Bundle, Bale & Pallet

After all these checks papers come to the market for selling. But have you ever seen paper being sold singly? No. Never. This is because it is not commercially viable to sell one sheet of paper for a price. It is always sold in stacks, and the amount varies depending on the size, the number of sheets in the stack and the gsm (grams per square meter) of the paper and sometimes also the material used in making the paper and its quality.

These together decide the cost of manufacturing paper and further the selling price to make it economically viable. And mostly, the number of Papers is not measured in the number of sheets. Like, you cannot just go out and buy 579 sheets of ARE Paper if you need that many for your work.

Like there are Standardized Sizes of Paper, there are Standardized Quantities for defining the number of papers as well. So, when buying paper, it is essential to know the number of sheets available in each of these Standard Quantities for Number of Papers or Paper Quantities . The most used quantities are reams, quires, bundles, bales, and pallets. We are going to talk about these today.

Paper Quantities – Ream, Quire, Bundle, Bale, Pallet and Other Quantities

Modern (metric) paper quantities.

Metric Quantities means the quantities that have been standardized for international usage, and they mean the same when you go to any part of the world. Although the quantities mentioned above earlier varied in use from country to country – which we will talk about later – recently, for modern usage and ease, the Paper Quantities – quires, reams, bundles, and bales – have been standardized. The number of sheets in each of these quantities are as stated below:

If you desire to convert between two different quantities amongst quires, reams, bundles, and bales, then the conversion can be done as follows:

1 Bale = 200 Quires
1 Bale = 10 Reams
1 Bale = 5 Bundles
1 Bundle = 40 Quires
1 Bundle = 2 Reams
1 Bundle = 0.2 Bales
1 Ream = 20 Quires
1 Ream = 0.5 Bundles
1 Ream = 0.1 Bales
1 Quire = 0.05 Reams
1 Quire = 0.025 Bundles
1 Quire = 0.005 Bales

Pallets of Paper

Although Pallet is used in many countries, as this quantity is very new and recent, it has not been standardized yet. Hence, pallet varies from country to country as follows:

US – 40 cases of 10 reams per case. That is a total of 200,000 sheets.
UK – 20 boxes of 5 reams per case , a total of 50,000 sheets OR 50 boxes of 5 reams per case, a total of 125,000 sheets depending upon the seller.

Other Paper Quantities

Papers are also sold in the following stacks:

100 Sheets (4 Quires) Package for Specialist Papers.
250 Sheets (10 Quires) Package for heavier weight (160 gsm+) Card Papers.

Imperial (Old) Reams and Quires

Before the standardization of Paper Quantities in the Metric Quantities, 1 Quire was used to refer to a stack of 24 Sheets and 1 Ream for a stack of 20 Quires (480 Sheets). This quantification of 1 Quire was also used in the US, and it was referred to as the short quire. This was likely because 1 Dozen is defined as a group of 12 things and this was one of the standards used in those countries earlier. A list of paper quantities used in the Old times are as follows:

Even though the number of sheets of paper in each of these paper quantities were different, the relative number of either of these paper quantities in another of them have remained the same and hence, the conversions between any two of these paper quantities can be done using the information that we have stated earlier under the Metric Paper Quantities heading.

The Printer’s Ream

The Printer’s Ream was more significant than an ordinary ream. People use it to avoid an obstacle in the printing process of a ream of paper due to wastage. Also, the old ream was of 480 Sheets of Paper, but a Printer’s Ream is of 516 Sheets of Paper. The extra 36 Sheets were for the replacement of the wasted or blotted sheets. But, after the standardization of the ream to 500 Sheets of Paper, Printer’s Ream was removed from usage.

Weight of Sheets & Reams Calculator

You can find more information about paper weights here .

What is the quantity of a ream?

500 sheets. A standard portion of the paper contains 20 queries or 500 sheets(before 480 sheets) or 516 sheets(printer's heap or perfect heap).

How many reams of paper are on a pallet?

Most pallets of paper in the U.S. include 40 cases, each of that is today, permeated following 10 reams. That resources a pallet containing 400 reams or 200.000 sheets of paper.

What is a quire of paper?

A build-up of 24 or 25 sheets of paper of the same crest and characteristic: individual twentieth of a heap.

How do you calculate paper ream?

To decide the heap pressure of some likely diameter coating, multiply the square inches in the likely size for one likely essential weight, and separate the result apiece square one-twelfth of a foot/2.54 centimeters measured field of the elementary capacity.

Conclusion:

Now you know everything there is to know about paper quantities. So, the next time someone asks about them, you’ll be ready to let them know!

As an author for papersize.co, Alan Lee showcases his exceptional ability to distill complex ideas regarding sizes of paper into accessible and compelling narratives.

Amber Robertson

Amber Robertson is the founder of Quill and Fox. A creative writing studio that helps people find their voice and share their stories. Amber is also a published author, with her first book slated for release in 2020. She loves spending time with her family and friends, reading, writing, and traveling. When Amber was younger, she loved to write short stories and plays. But somewhere along the way, she lost touch with her creativity. It wasn’t until she became a mom that she realized how important it was to share her stories—both the good and the bad—with the people she loves most. That’s when Quill and Fox was born. Amber is passionate about helping others find their voice and share their stories. She believes that every person has a story worth telling, and it’s her mission to help them tell it in a way that is authentic and true to themselves

How Many Reams of Paper in a Box: A Comprehensive Guide

Table of Contents

As we move towards a paperless society, we can’t deny the importance of paper in our daily lives. Whether it’s for printing documents, creating artwork, or packaging products, paper is still a crucial component in various industries. However, one common question that arises is, “How many reams of paper are in a box?”.

Understanding the number of reams in a box is essential for both businesses and individuals who use paper regularly. It helps them plan their purchases and budget accordingly, reducing unnecessary expenses. In this article, we’ll discuss everything you need to know about paper reams and the number of reams in a box.

Understanding Paper Reams

Before we dive into the number of reams in a box, let’s first understand what a paper ream is. A ream of paper is a standardized quantity of sheets of paper, usually 500. The exact number of sheets in a ream may vary depending on the type of paper and its size. For example, a ream of legal-sized paper (8.5 x 14 inches) may contain 500 sheets, while a ream of letter-sized paper (8.5 x 11 inches) may contain 550 sheets.

Knowing the number of sheets in a ream is crucial as it helps you determine the quantity of paper you need for a specific task. Moreover, it also helps you compare prices between different brands and types of paper based on their cost per sheet. For instance, if you want to buy a ream of paper for $5, and one brand has 500 sheets while the other has 550 sheets, the latter would be a better deal as it costs less per sheet.

In the next section, we’ll discuss the different types of paper boxes and their sizes.

Types of Paper Boxes

Paper boxes come in various shapes and sizes, depending on the manufacturer and the intended use. Some common types of paper boxes include:

Standard paper boxes: These are the most common type of paper boxes used for storing and transporting paper. They are rectangular in shape and come in different sizes.
Copier paper boxes: These are specifically designed to store copier paper and come in the standard size of 11 x 17 inches.
Printer paper boxes: These are designed to store printer paper and come in different sizes depending on the printer’s paper tray size.
Specialty paper boxes: These are designed to store specialty papers such as cardstock, photo paper, and glossy paper.

Paper boxes are labeled with information such as the size, weight, and number of reams they contain. The most important information to look for is the number of reams in the box.

Determining the Number of Reams in a Box

Determining the number of reams in a box is a simple process. Here’s a step-by-step guide on how to calculate the number of reams in a box:

Look for the label on the paper box. The label should indicate the weight, size, and number of reams in the box.

Determine the weight of the paper in the box. Most paper boxes are labeled with the weight of the paper in pounds.

Divide the weight of the paper by the weight of a single ream. For example, if the weight of the paper is 20 pounds, and the weight of a single ream is 5 pounds, you would divide 20 by 5, which equals 4.

The result of the division is the number of reams in the box. In this example, the box contains four reams of paper.

Here are some examples of calculations for different box sizes:

A box of standard letter-sized paper (8.5 x 11 inches) labeled as “20 lb., 92 brightness, 10 reams” contains 5000 sheets of paper, or 10 reams of 500 sheets each.
A box of legal-sized paper (8.5 x 14 inches) labeled as “24 lb., 98 brightness, 5 reams” contains 2500 sheets of paper, or 5 reams of 500 sheets each.

By following these simple steps, you can quickly determine the number of reams in a box and make informed decisions when purchasing paper.

Importance of Knowing the Number of Reams in a Box

Knowing the number of reams in a box can have several benefits. Firstly, it helps you plan your paper usage and purchase accordingly, reducing the likelihood of running out of paper when you need it the most. It also helps you avoid overbuying, leading to unnecessary expenses and storage issues. For businesses, it can prevent overstocking and reduce the risk of paper wastage due to damaged or expired stock.

Moreover, understanding the number of reams in a box can help you compare prices and choose the best deal. By knowing how many sheets are in a ream, you can calculate the cost per sheet and compare it across different brands and types of paper. This allows you to make an informed decision and save money in the long run.

In conclusion, understanding the number of reams in a box is crucial for anyone who uses paper regularly. It helps you plan your purchases, reduce expenses, and avoid wastage. By knowing the number of sheets in a ream, you can also compare prices and choose the best deal. So next time you’re buying paper, don’t forget to check the number of reams in a box and make an informed decision.

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Quick Question Monday : What is Price Per M in Price Quotes?

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You might have received price quotes from different industries where price is expressed in $/M, and you may be wondering, what's M? What's the unit of measure here? Why it is done this way? And why do they use the uppercase letter M?

What is M and what does it mean?

While this may very well be the better option for a larger item costing more per unit (it wouldn't make much sense to quote a car per thousand ($15,000,000,000/M) since the price is so large per unit, it is better to quote in $/M when you are dealing with smaller case per unit and when items are not often sold in single units. You will find this quoting method common in printing and the online media industry. For example, paper mills often quote in this unit to help compare apple to apple ($26.15/M for 50 lbs. paper vs. $30.22/M for 70 lbs. paper). This unit is also common in the online media industry where banner advertising or email marketing is sold at CPM (cost per thousand impressions).

Likewise in the packaging industry, where bottles or closures are often sold at tens of thousands, and different manufacturers having different carton and pallet counts (number of bottles or closures packed in a carton and on a pallet), it will be more sensible to quote per thousand units. Hence this quoting mechanism is used. For example, let's say you are responsible for obtaining a quote for a 1oz Amber Boston Round Glass Bottle, and your product line has an annual usage of 250,000 units and initial release quantity of 50,000 units.

You may see a price quote for 50,000 1oz Amber Boston Round Glass Bottles at $352.51/M, which means $352.51 for one thousand bottles, if the price quote was given in each ($/ea.), you will then see $0.35251/ea., which seems silly given the number of decimal points in this currency format. It also makes for a harder comparison when you then receive an alternative quote of the same bottle, from a different manufacturer, at $351.12/M, or $0.35112/ea. If you begin making comparisons on price and the rounded down decimal to reflect proper currency, the two prices at each ($0.35251/ea. and $0.35112/ea.) will become ($0.35/ea. and $0.35/ea.), making the two quotes the same. Now compare the two quotes at $/M : ($352.51/M and $351.12/M), that's a difference of $1.39/M. While $1.39 doesn't seem like much, multiplying that by the total units you are buying annually (250,000), you will begin to see why such as small difference in $/M begins to make an impact in your overall supply chain.

This is not to say that every item in the packaging industry quotes units per thousand, and for a smaller quantity (carton) or larger items (gallon drums, plastic pails, etc.) it is better to quote $/ea. as they are being sold individually.

Ok, I can understand that. But where did the M come from?

IV is 4 but VI is 6
XVIII is 18 (X is 10 V is 5 and III is 3, the III goes after V makes it 8 [VIII], and that going after X adds to it to become 18)
MMXV is 2015 (two Ms makes it 2,000, X is 10 and V is 5, and you can put them all together to make it 2015)

Since we are not roman numerals experts, it is best to leave it to the experts to help you understand how roman numerals work, just in case you come across this article while studying for your roman numeral exam:

Roman Numerals Chart
Roman Numerals - Wikipedia
Roman Numerals Chart 1 - 100 - Roman-numerals.org

If you are still unsure about reading Roman Numerals, numbers are formed by combining symbols and adding the values. In this alphabet there is no zero, symbols are placed from left to right in order of the value that they represent. There are a few exceptions to the rule, but other than that the rules are fairly simple.

Why not K for thousand since many associate M with million?

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Two-Leaved Standard Dimension Paper / Quantity Takeoff Sheet for Construction Estimating

3 Types of Dimension Paper / Takeoff Sheets Used by Quantity Surveyors, Building Estimators and Engineers.

By admin in Estimator’s Tools , Notebooks , Quantity Surveying Notebook

No Feint A4 Standard Dimension Paper – 13_15_15_Single Leaved

A dimension paper also known as a takeoff sheet or measurement sheet is used to enter measurements taken off from an architectural drawing or building plan. The traditional quantity takeoff sheet in the form of A4 paper is widely used at professional learning institutions of quantity surveying, but it’s also used by consulting quantity surveyors, engineers, contractors and building estimators.

Although estimating and quantity takeoff software has superseded paper because of its speed and ability to reduce production time by as much as 80%, dimension papers still find their use on and off the site. It’s much more practical, convenient and user-friendly to carry your dimension pad or measurement notebook to the site, than your laptop or tablet, which may shut down due to a flat battery, malfunction, get damaged by dropping to the ground and get hit by falling objects.

An electronic touchscreen is not easy to work with in the open field because of the sun glare and the attention it requires in entering measurements on the device. You also have to save the digital entries each time. In this case, most people will naturally choose to work with their familiar notebook and pen, since it’s much easier and user-friendly.

Dimension pads are sold at stationery and office supply stores. Each dimension pad has about 50, 100, 150 or 200 A4 dimension sheets bound to the head. The softback pad can be folded over its back, allowing you to write notes and entries conveniently in the field. The sheets are either plain or ruled on one side depending on the type, weighing around 60 to 80gm/m2. White bond paper is used in most cases, and if they are ruled sheets, you can choose from options listed below:

Feint and Margin paper – This is a sheet with feint (light coloured) horizontal lines, as well as margins (vertical lines).

Paper with Margins and No Feint – This is a sheet with no feint or any horizontal lines. It only contains vertical lines and margins.

No Feint A4 Standard Dimension Paper – 13_15_15_Double Leaved

The vertical lines and margins of a paper sheet forming the columns are usually darker than the feint lines (horizontal lines) to make them more visible and outstanding.

Now that you have an idea of the two general types of Ruled Dimension Papers, we can further classify them according to Page Layouts. There are two main layouts for the standard quantity surveying takeoff sheet recommended by the system of measurement. Outside of the quantity surveying field, a non-standard form is usually used by engineers and building contractors.

Macron Venter Quantity Takeoff Pad / Measurements Notebook

Quantity Takeoff Pad with 60 Standard Dimension Sheets [Sidebound Pad] – Buy Now on Amazon $7.50

Quantity Takeoff Pad with 100 Standard Dimension Sheets [Sidebound Pad] – Buy Now on Amazon $12.00

Quantity Takeoff Pad with 150 Standard Dimension Sheets [Sidebound Pad] – Buy Now on Amazon $14.50

Quantity Takeoff Pad with 200 Standard Dimension Sheets [Sidebound Pad] – Buy Now on Amazon $16.50

The Two-Leaved Standard Dimension Paper .

This standard dimension paper is an A4 paper (size 210X297mm) (8.25×11.75 inches) with a double sided page. The Left and Right side of the standard takeoff paper has 4 columns each.

Two Leaved Standard Dimension Paper with Feint and Margins

Each side has the following menu:

First column – Timesing column (for entering multiplication factors or constants)

Second column – Dimension column

Third column – Squaring column (also known as the summation column)

Fourth column – Description column (For item descriptions and waste calculations)

Note**A dimension paper must provide space for the binding column on the left side/margin. This is a margin for binding the sheets which prevents obstruction with the timesing column.

The Single-Leaf Standard Dimension Paper.

This is an alternative standard dimension paper, type A4 (size 210X297mm) (8.25×11.75 inches), but unlike the Two-Leaved standard takeoff paper, the Single-Leaf paper is a document with a single-sided page.

Single Leaved Standard Dimension Paper with Feint and Margins

This paper has 5 columns, excluding the binding column:

Fifth column – Annotation column (For explanatory notes)

The Description column and Annotation column are nearly the same width. The timesing, dimension and squaring columns will maintain the same width as in the Double-Leafed document.

One of the features of a standard quantity surveying takeoff paper is that dimensions are entered vertically along the column in the order LWH (Length, Width, Height).

Measurement Sheet for Building Contractors and Engineers

This is a non-standard dimension sheet , mostly used by engineers and building contractors. Printed on A4 paper, it has 8 columns excluding the binding column. The columns are:

Engineer/Contractor’s Dimension Measurement Sheet with Feint and Margins

First column – Bill Item number.

Second column – Description column (For item descriptions and waste calculations)

Third column – Timesing column also called the Number column (for entering multiplication factors and enumerated items)

Fourth column – Length column (Dimension column for Length)

Fifth column – Width column (Dimension column for Width)

Sixth column – Height column (Dimension column for Height or Depth)

Seventh column – Quantity column also called the Summation column

Eight column – Total column (For entering the item total quantity).

No Feint A4 Pad 13_15_15 Measurement Sheet for Building Contractors and Engineers

This general measurement sheet is also a digital format widely used in quantity takeoff software such as DimensionX, QSPlus, WinQS and CostX.

Other Details of a Dimension Paper

A quantity takeoff paper should also include fields for the Project Name, Page Number, Date and Company Name on the header.

Spacing of Lines

Ruled paper for takeoff sheets must have:

Feint line spacing of 6.1mm or 7.1mm

Spacing for Timesing,Dimension and Squaring columns – 15mm maximum

Spacing for Description column – 53mm

Head Bound or Side bound Pad?

If the dimension pad is head-bound, maximum spacing should be allowed for the Timesing, Dimension and Squaring columns. In this case, 15mm is the maximum spacing.

If the dimension pad is side-bound, room should be allowed for the binding column. In this case, the spacing for the Timesing column can be reduced to about 10mm in width, opening up a binding space of 20mm for a Two-Leaved standard dimension sheet.

A Single-Leaved standard dimension sheet has lots of room to accommodate a binding column, which can be obtained by shifting the first 3 columns to the right without adjusting the Timesing column.

Binding column width – 20mm

Binding header – 20mm

Project Details header – 28mm

Macron Venter vs Vestry Takeoff Paper Sheets

The Vestry CV5068 A4 Survey Pad (100 sheets, No Feint, 60gsm) is a typical two-leaved standard dimension pad for quantity surveyors and building estimators. This paper is currently out of stock in many stores and very hard to find. Vestry produces a variety of survey pads, so you have to know the right kind of pad for your needs and profession. The product code and picture of the actual dimension sheet should tell you if it’s the right pad.

Dimension pads produced by Macron Venter are uniquely designed and clearly defined for a specific profession and purpose. Whether you are a quantity surveyor, building estimator, contractor, land surveyor, civil engineer, structural engineer, cost engineer, architect or accountant, you will find the right measurement pads, field books, journals, log books and notebooks for you.

PROPERTIES OF PAPER

This page contains various properties of paper, how these properties are measured and how are they relevant to end user and/or papermaker. Under TAPPI standard all tests are carried out at 23 0 C ± 1 0 C and 50 + 2% relative humidity.

Click here for a List of Paper Testing Service Provider and Testing Equipment Manufacturers

Physical Properties

For more details on Dimensional Stability, please read Dimensional Stability Notes by Chuck Green

Not so good formation Good formation

Optical Properties

Shade: Shade is a measurement of the color of paper. Shade is defined using a universally accepted color measurement model.Shade represents the subtle differences in color within the visible spectrum.

Technically, shade is an important characteristic within the definition of a paper's whiteness. Shade, particularly in color printing, can directly impact the correct look and feel of the printed images.

For paperboard finished is designated by numbers ranging from 1 to 4. N0. 4 is highest possible machine finish and No.1 is fairly rough surface.

Machine Finish : A finish obtained on the paper machine. It may be high or low.

English Finish : This is a special machine finish that is quite high but one which is obtained without too much gloss.

Glazed Finish : This finish is obtained by calendering moist paper under high pressure.

Machine-glazed Finish : This finish is obtained by drying the sheet against a highly polished metal drying roll known as Yankee Cylinder.

Smooth Finish : This finish is obtained by the use of pressure rolls or a breaker stack in the dryer section of the paper machine.

Antique Finish : This is rough finish is obtained by not calendering the paper.

A paper with a relatively high opacity at 96% and above will have almost no show- through from printing on the reverse side or the sheet below. Selecting a paper with high opacity is specially important if the printing includes solid block of colors, bold type and heavy coverage.

Strength Properties

Softness : Softness is the lack of hardness when paper is crumbled in hand. Softness is also used in opposition to hardness as evaluated by compressibility. Softness is an important attribute of sanitary tissues, facial tissues and towelling, where it is related to the feel of paper against the skin. Softness is important in glassine and wax papers, in which it is related to the ease of folding.

Hardness and Compressibility: Hardness is the property of paper that causes it to resist indentation by another material. Normally a soft cooked pulp will produce soft paper and vice-versa. Compressibility is defined as the reciprocal of the bulk modulus. It can be measured under static load by determining the change in caliper of the sheet under and expressing the results as a function of pressure.

Droop Rigidity CD : Droop rigidity measures the stiffness of the paper or board, more often applied to lighter weight grades. CD refers to cross direction, and MD to machine direction, Droop rigidity is higher in the machine direction. The higher the value the stiffer the paper.

Droop Rigidity MD : Droop rigidity measures the stiffness of the paper or board, more often applied to lighter weight grades. CD refers to cross direction, and MD to machine direction, Droop rigidity is higher in the machine direction. The higher the value the stiffer the paper.

Bending Resistance/ Stiffness (Lorentzen &Wettre): It is a measure of the resistance offered to a bending force by a rectangular sample, expressed in mN (milli Newtons). The standards are as per TAPPI T 556.

Breaking Length (km) = 102*T/R or 3.658*T 1 /R 1

T = Tensile Strength, kN/m T 1 = Tensile Strength, lb/inch R = Basis Weight, g/m 2 R 1 = Basis Weight, lb/1000 ft 2

Tensile Index (Nm/g) = 1000*T/R or 36.87*T 1 /R 1

Z Direction Tensile Strength: Or internal bond strength provides an indication of strength of board in relation to glue bonding at carton side seams and possible Delamination on scoring, or use of high tack coating. The procedural standards are explained in TAPPI T 541.

Zero SpanTensile Strength (Paper): This provide an idea of tensile strength of fiber and not the strength of fiber bonding. The gauge length of the tensile strength measuring instrument is set to zero so the failure is by fiber rapture only. It is measured with a strip of paper but mainly a pulp property.

Miscellaneous Properties

The number of specks of each area are expressed either as mm 2 /Kg for pulp or mm 2 /m 2 for paper

T he pH value of -->paper --> can be determined by :

- Disintegrating the paper in hot distilled water and determining the pH of the extract. - Disintegrating the paper in cold distilled water and determining the pH of the extract. - Directly using a wet electrode on the paper surface.

These 3 methods measure different solutions and so give different pH values.

Print Quality

Thermal conductivity is a measure of how easily heat passes through a particular type of material. Thermal conductivity is measured in watts per meter Celsius. Because the conductivity of materials can vary with temperature, no one single value exists for the conductivity of paper. However, under standard temperature and pressure of 25 degrees Celsius and 1 atmosphere, the thermal conductivity of paper is 0.05 watts per meter Celsius or 0.03 BTU ft/hour. Sq. ft 0 F.

Specific Heat Capacity of Paper: The specific heat capacity of a material is a measure of the amount of energy required to raise the temperature of a specific quantity of that material by a specific amount. The units of specific heat capacity are Kilojoules per Kilogram Celsius. The specific heat capacity of paper is 1.4 Kilojoules per Kilogram Celsius or 0.33 Btu/lb/ 0 F.

CORRUGATED BOARD

* “Related” does not imply “equivalence.” A “Related Standard” may be a standard for a similar property, but this should not assume identical technical content or matching results.

Go to http://www.tappi.org/content/pdf/standards/subject_index_tms.pdf for a complete list of TAPPI testing standards.

Reporting Units for Physical Testing Procedures for Paper Testing

1 Many physical testing units will not be changed by the conversion to metric or SI units. Thus, such tests as brightness (%), compressibility (%), Standard Freeness (ml), opacity (%), and stretch (%) will continue to be reported in the dame units. 2 Most of the suggested reporting units in SI metric terms are based on recommendations from the British Paper Makers' Association. 3 Some properties will continue to be reported in present units. Thus, such procedures as the Bendtsen air resistance and smoothness tests and the Sheffield smoothness test will continue to be reported in ml/min. 4 If the given trade size is in 480 sheets, then factor shall be multiplied by 48/50 (or 0.960).

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Open Access

Peer-reviewed

Research Article

Quantity and/or Quality? The Importance of Publishing Many Papers

* E-mail: [email protected]

Affiliation KTH Royal Institute of Technology, INDEK, SE-100 44 Stockholm, Sweden

Affiliation VU University Amsterdam, Network Institute & Institute for Social Resilience Amsterdam, Amsterdam, The Netherlands

Ulf Sandström,
Peter van den Besselaar

Published: November 21, 2016
https://doi.org/10.1371/journal.pone.0166149
Reader Comments

Do highly productive researchers have significantly higher probability to produce top cited papers? Or do high productive researchers mainly produce a sea of irrelevant papers—in other words do we find a diminishing marginal result from productivity? The answer on these questions is important, as it may help to answer the question of whether the increased competition and increased use of indicators for research evaluation and accountability focus has perverse effects or not. We use a Swedish author disambiguated dataset consisting of 48.000 researchers and their WoS-publications during the period of 2008–2011 with citations until 2014 to investigate the relation between productivity and production of highly cited papers. As the analysis shows, quantity does make a difference.

Citation: Sandström U, van den Besselaar P (2016) Quantity and/or Quality? The Importance of Publishing Many Papers. PLoS ONE 11(11): e0166149. https://doi.org/10.1371/journal.pone.0166149

Editor: Pablo Dorta-González, Universidad de las Palmas de Gran Canaria, SPAIN

Received: April 29, 2016; Accepted: October 19, 2016; Published: November 21, 2016

Copyright: © 2016 Sandström, van den Besselaar. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: The raw data file used in this study is based on downloads from Online Web of Science ( webofknowledge.com ) using the following query (CU=Sweden AND PY=2008-2011 AND DT=(Article OR Letters OR Reviews or Proceedings Papers)). From the online database we have retrieved all data. These data are publicly available to customers with a subscription to WoS, e.g., through the university library. All calculations of data are described in the article.

Funding: The work was supported by the following: P12-1302:1 http://www.rj.se ; ERC grant 610706 https://erc.europa.eu . The funders had no role in study design, data collection and analysis, decision to publish, or preparations of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

One astonishing feature of the scientific enterprise is the role of a few extremely prolific researchers [ 1 ]. Thomson Reuters gather them in the Highly Cited Researchers database, where they are listed and recognized per area. Using another database, Scopus , Klavans & Boyack phrase them ‘superstars’ in a large-scale study of publication behaviour, thereby showing that superstars publishes less in isolated areas (retrieved using a clustering procedure), in dying areas, or in areas without an inherent dynamics [ 2 ]. Highly productive and cited researchers tend to look for the new opportunities. Obviously, the highly productive researchers have to be taken into consideration for many reasons, both for science policy and for scholarly understanding of how the science system works.

Within bibliometrics there is a discussion on how to identify and measure “superstars”, and many papers discuss the correlation between the various indicators developed for performance measurement. One of the stable outcomes is that there is a high correlation between the numbers of papers a researcher has published and the number of citations received [ 3 ]. From that perspective, both indicators tend to measure the same attribute of researchers, as is actually materialized in the introduction of the H-index [ 4 ]. The progress of science rests on the huge amount of effort and publications, but the number of real discoveries and path breaking new ideas is rather small. This has led to a different focus, and the discussion about impact has shifted from counting numbers of citations to more qualified types of citations and weighted publications. Instead of counting publications and citations, the decisive difference in this perspective is whether a researcher contributes to the small set of very high-cited papers. Different thresholds are deployed, from the top 1% highly cited papers to the top 10% highly cited papers or with the CCS method proposed by Glänzel & Schubert [ 5 ]. Generally speaking, only when a paper reaches such a citation level, it contains a distinctive result that contributes to scientific progress. Increasingly, performance measures take this selectivity into account, and when calculating overall productivity and impact figures for researchers, papers (productivity) and citations (impact) are weighted differently depending on the impact percentile the paper belongs to [ 6 ].

If one agrees that in science it is all about top (cited) publications, the question comes up what an efficient publication strategy would look like. Is publishing a lot the best way–or does that generally lead to normal science , Kuhn [ 7 ], with only low impact papers? The total number of citations received may still be large, but no top papers may have been produced. This was already the core of Butler’s critique on the Australian funding system [ 8 ] and is also the underlying idea of emerging movements in favour of ‘slow science’ like e.g. in the Netherlands; there the ‘science in transition’ movement [ 9 ] was able to convince the big academic institutions to remove productivity as a criterion from the guidelines for the national research assessment (SEP). The underlying idea is that quality and not quantity should dominate–and that with all the emphasis on numbers of publications, the system has become corrupted, see the discussion in The Leiden Manifesto (Hicks et al. [ 10 ]), and the Metric Tide report (Wilsdon et al. [ 11 ]).

However, others seem to see this differently. Firstly, recent empirical research suggests that on the long run, average output per researcher (corrected for the number of co-authors) has not increased at all [ 12 ]. This suggests that much of the debate on output indicators and output funding leading to perverse effects may be wrongly directed. Secondly, in his work on scientific creativity, Simonton has extensively argued that (i) having a breakthrough idea is a low probability event that happens by chance, and therefore that (ii) the more often one tries, the higher the probability to have a ‘hit’ so now and then [ 13 ]. Also other contextual factors influence the chance for important results, but overall, the number of tries (publications) is the decisive variable. This would also explain why Nobel laureates often have many more publications than normal researchers. Zuckerman states that laureates publish at a much higher rate [ 14 ], and Sandström shows the early recognition of papers by later Nobel laureates [ 15 ]. The more often a researcher tries out an idea (and publishes it) the higher the probability that there is something very new and relevant, and atypical for the scientific community [ 16 ].

This brings us to the question what the relation is between overall output (number of publications) and the number of high impact papers of researchers. Several possibilities exist, and only the last two would be evidence that more is not better:

Increasing returns from productivity: The number of top papers increases faster than the total output (the purple line in Fig 1 ). So, the higher the total output of a researcher, the more he/she contributes to scientific progress in an absolute (number of top papers) and in a relative sense (share of top papers).
Constant returns from productivity: The number of top papers increases proportionally with total output (the green line in Fig 1 ). So the higher the total output of a researcher, the more he/she contributes to scientific progress in an absolute sense, but in a relative sense there is no difference.
Positive but declining returns from productivity: The number of top papers increases but less fast as total output (the red line in Fig 1 ). So the higher the total output of a researcher, the more he/she contributes to scientific progress in an absolute sense. However within the corpus the share of lower impact papers increases.
A limit to impact: It might be the case that for every researcher there is a limit to the number of good ideas that can be produced. Above some productivity threshold, papers will merely repeat already published ideas, and will not contain new or good ideas anymore. If that would be the case, above that productivity threshold the number of top cited papers remains about constant (the grey line in Fig 1 ).
Small is beautiful: Publishing a lot is detrimental to quality. Those who write a lot may have even less top papers than those that are more selective: small is beautiful, represented by the blue line in Fig 1 .

PPT PowerPoint slide
PNG larger image
TIFF original image

https://doi.org/10.1371/journal.pone.0166149.g001

So the focus of this paper is on the researcher and his/her oeuvre: does higher productivity result in a higher absolute and/or relative number of top cited papers? And the unit of analysis is not the paper: that is because a paper generally has more authors, who individually can be more or less productive. The answer to our question may inform our understanding of knowledge production and scientific creativity, but is also practically relevant for selection processes, and as explained above for research evaluation procedures: is high productivity a good thing, or a perverse effect and detrimental to the progress of science as it does not add to our knowledge, but only to a waste of paper?

Not much research on this issue is available. Abramo et al. [ 17 ] tried to answer the question by use of an Italian database of unique authors. They find only a moderate correlation between productive scientist and authors of highly cited articles. One obvious problem with their article is that they take for granted that top scientists work in solitude or with each other, but never work with younger and less experienced researchers. We will discuss that problem although we are not able to solve the problem in full in this paper.

Ioannidis et al. [ 18 ] showed that less than 1% of all researchers that published something (indexed in Scopus) between 1996 and 2011 did publish in each of these 16 years, and that this small set of core scientists are far more cited than others. They account for 41.7% of all papers in the period under study and 87.1% of all papers with >1000 citations. Also Kwiek shows that a large share of total publications comes from a relatively small group of high productive researchers, but does not go into the issue of quality of the papers [ 19 ]. Larivière & Costas do focus on top publications and they report stronger findings: “especially for older researchers (……) who have had a long period of time to accumulate scientific capital, there can never be too many papers.” [ 20 ]

Data and Methods

In order to answer our question, we use the 74.000 WoS-publications 2008–2011—with a citation window until 2014—of all researchers with a Swedish address using the following document types in databases SCI-E, SSCI and A&HCI: articles, letters, proceeding papers and reviews.

For identifying authors and keeping them separate we use a combination of automatic and manual disambiguation methods. An algorithm for disambiguating unique individuals was developed by Sandström & Sandström [ 21 ], and further developed by Gurney et al. [ 22 ]. It proceeds fast, although requires supplementary manual cleaning methods. The deployed method takes into account surnames and first-name initials, the words that occur in article headings, and the journals, addresses, references and journal categories used by each researcher. There is also weighting for the normal publication frequency of the various fields [ 21 ; 23 ].

As indicated the data covers 74.000 articles and 195.000 author shares that have been judged to belong to Swedish universities or other Swedish organisations. In a few cases, articles from people who have worked both in Sweden and in one or more Nordic countries have been kept together, and articles have thus been included even if they came into being outside Sweden (the process of distinguishing names is thus carried out at Nordic level). This was done as the academic labour market to quite a large extent is Scandinavian.

All articles by each researcher are ranked, based on received citations and according to the about 260 subject categories as specified in the Web of Science, and the articles are divided into CSS (Characteristic Scores and Scales) classes (0, 1, 2, 3). While measures based on percentile groups (e.g. PPtop1% etc.) are arbitrarily constructed, CSS have some advantages concerning the identification of outstanding citation rates [ 5 ]. The CSS method is a procedure for truncating a sample (e.g. a subfield citation distribution) according to mean values from the low-end up to the high-end. Every category of the CSS created using this procedure helps to identify papers that fulfil the requirements for being cited above the respective thresholds. In this paper we will use two levels, level CSS1 and CSS3, which in the former case cover the 37% most cited papers, and in the latter case the about 3.5% of most cited papers: the “outstandingly cited papers” [ 24 ].

In the following we will investigate the relation between quality and quantity in several different ways. We do this, as from a methodological perspective different options are open, without a convincing argument which one would be the better. By using a variety of methods, we avoid to produce results that are only artefacts of a specific method.

We investigate whether the number of CSS3 papers increases with productivity (purple, green, red line in Fig 1 ), and whether the share of CSS3 papers as part of all papers increases with productivity (the purple line in Fig 1 ). A main issue is whether there is a CSS3 ceiling (the grey line in Fig 1 ), or whether high productive authors actually have a low impact, and whether small is beautiful (the blue line). We first calculate the average number of CSS3 papers, given the productivity level of authors. In order to do so, we classify all about 48.000 Swedish researchers into productivity classes: productivity class 1 has one publication in the four years period under study, class 2 has two, class 3 has three to four, class 4 has five to eight, class 5 has nine to sixteen, class 6 has seventeen to 31 publications, and finally class 7 covers researchers with 32 or more publications. The classification bins have been sized to be roughly even on a logarithmic scale. For each of these classes, we calculate the average number of papers in the CSS3 class. This is done for the whole set, and for the eight distinguished research fields separately ( Table 1 ) based on a classification developed by Zhang et al. [ 25 ] (the field of humanities added to the classification by us). Publications are integer counted, and citations are field normalized. The average number of papers in CSS 3 is not an integer, as on average only one out of some 30 papers belongs to CSS3.
We do a regression with the total number of integer counted (IC) publications of an author as the independent variable, and the also integer counted number of top cited publications of the same author. We do this for each of the definitions of ‘top cited’ that were discussed above, using field-normalized citations (using normalization to subject category, publication year and document category). This is done for the total population of (publishing) researchers, without normalizing for field-based productivity differences. As the total set of researchers is dominated by life and medical sciences and by natural sciences, and as these groups have comparable average publications and citations, we assume that this does not influence the results. However, under point (iv) below, we introduce a way of taking field differences in productivity into account.
We do the same analysis as under (ii), but use fractional instead of integer counting of publications and top-cited publications. This helps to investigate the effect of different ways of counting on the relations under study.
We introduce field-normalized (fractional counted) productivity, and calculate the relation between in this way defined productivity and having at the number of fractionally counted publication in CSS1 and CSS3. As we produced field normalized output counts, we can provide an integrated analysis of all researchers across all fields. This is done with a method–Field Adjusted Production (FAP)—based on Waring estimations. This method was initially developed by Glänzel and his colleagues [ 26 , 27 ], during the 1980s, and further explained and tested in Sandström & Sandström [ 21 ], see also [ 23 ]. Basically, the method is used in order to compensate for differences in ‘the normal rate of scholarly production’ between research areas. To this end, all journals in the Web of Science have been classified according to five categories (applied sciences, natural sciences, health sciences, economic & social sciences, and art & humanities). Note this is a different classification than the one used above. This is because for productivity, the distinction between basic and fundamental should be more explicitly taken into account. We collapse some fields, but split everywhere applied research from basic. This categorisation of journals into macro fields is based on Science Metrix classification of research (< http://science-metrix.com/en/classification >).

https://doi.org/10.1371/journal.pone.0166149.t001

(i) Does the probability of high-cited papers increase with productivity?

We calculated for each of the seven productivity classes the average number of CSS3 papers ( Table 1 ). So, in productivity class 1 of Agricultural and Food science, researchers have published 1 paper in the period considered, and on average they have 0.03 paper in CSS3. In productivity class 2 of Agricultural and Food Science, authors have 2 papers and on average 0.08 papers in CSS3. Where the highest productivity classes are too small, they were combined with the next lower level. Inspecting Table 1 shows that for all fields the CSS3 score increases with productivity–only for the Humanities we found that the score in the highest productivity class 4 is slightly lower than in the productivity class 3, and for computer science & mathematics it is equal. So in general, the higher the productivity of a researcher, the more top-cited papers a researcher has.

In Fig 2 we show the relation between productivity and authoring top cited papers (from Table 1 ) graphically, which makes it easier to compare the found patterns with the model of Fig 1 . Fig 2 suggests increasing returns from productivity for the Sciences & engineering, the Life sciences, and for Psychology. A constant return from productivity is found for Environmental sciences & biology as well as for Agricultural science related fields. The Social sciences show decreasing returns, and finally, Computer science & mathematics and the Humanities show a ceiling for top cited papers. For the latter fields it should be noted that the output we take here into account (journal articles) may not be representative enough. Furthermore, these disciplines also have characteristics that may be relevant here [Whitley 28 ]. For example, fields like social sciences, humanities, and computer science have different audiences than only peers: the general public, professionals, policy makers etc. If especially the stars do publish often for those non-peer audiences, their total output increases, but this may not result in additional citations.

https://doi.org/10.1371/journal.pone.0166149.g002

Are the differences between the productivity classes statistically significant? Anova tests show that the means of the number of CSS3 publications differ between the classes for all fields ( Fig 3 ). Anova test for means of the share of CSS3 publications does not result in significant differences between class 2 and class 3, and between class 5 and class 6 ( Fig 4 ). But over the whole range, also the share of top cited papers increases with output. So, more seems indeed better. Data are rather skewed and the Levene Test indicates no homogeneity of variance, therefore non-parametric tests were used as well. We tested whether the medians of the different productivity classes are significantly different, and use the Kruskal-Wallis test of the mean rank differences of the number and share of CSS3 papers between the productivity classes. This leads to the same findings as the Anova’s.

https://doi.org/10.1371/journal.pone.0166149.g003

https://doi.org/10.1371/journal.pone.0166149.g004

Repeating the same analysis for the individual fields gives similar outcomes for means and medians, although the differences are (because of the smaller number of cases in each of the fields) more often non-significant. The estimated means of the number and share of CSS3 papers for the individual fields, as well as the 95% confidence levels are in Supporting information. The main ‘deviant’ patterns are for computer science, for the humanities and for the social sciences, where the highest productivity classes actually have a lower share of CSS3 papers than the one but highest class–as was also visible in Fig 2 .

(ii) The effect of productivity on the number of high-cited papers

We have done a regression analysis with high-cited papers as dependent variable, and productivity as independent variable. We did the analysis for the various definitions of top cited papers. For papers in the top 1% cited papers ( Fig 5 ) the correlation is about 0.5. For the CSS3 ( Fig 6 ), the top 10 cited papers ( Fig 7 ), and the CSS1 classes ( Fig 8 ), the correlations are 0.58, 0.78 and 0.88 respectively. These correlations are fairly high.

https://doi.org/10.1371/journal.pone.0166149.g005

https://doi.org/10.1371/journal.pone.0166149.g006

https://doi.org/10.1371/journal.pone.0166149.g007

https://doi.org/10.1371/journal.pone.0166149.g008

The lower the citation threshold the higher the correlation. Why this is the case needs further investigation. One may conclude that the higher the level of citations, the more randomness in the data. However, a probably more obvious explanation is that the small number of high productive researchers with many top papers always have co-authors to these high cited papers who themselves are not highly productive, and may be in the science system only for a few years. This could be PhD students, temporary research staff, or post docs who e.g. have not pursued an academic career and stopped publishing. In that sense one also expects top cited authors in the lower productivity segments, reducing the explained variance. To control for this effect, one may include only PIs in the analysis, something we will address in a subsequent study.

Why would this effect be stronger for the higher citation threshold? This is related to the distribution of productivity. As generally is the case in bibliometric distributions [ 29 ], also in our population a small share of all authors produces a large share of the papers and even a larger share of the highly cited papers. For example, the 6.3% most productive researchers in our population (this is everybody with more than eleven publications in four years) are responsible for 37% of all papers and for 53% of the top 1% cited papers. And some 93% of the authors in our sample have no CSS3 top cited paper in the period under consideration,also these figures support the hypothesis that quantity makes a difference. So the higher the threshold, the larger the number of authors that have zero top cited papers also those that have top cited papers in the less selective sets (CSS1, top 10%). The latter authors now score zero and ‘move’ to the X-axis. This increases the dispersion of the data points–and consequently the correlation decreases.

This effect is also stronger if there are more co-authors per paper. This is easily understood, as the more co-authors a top paper has, the more not productive co-authors exist that do have co-authored top-cited papersWe may conclude that co-authoring equalizes and is not beneficial to the small elite. Depending on the field, between 92% and 98% of the researchers does not have a single paper in the CSS3 class in the four years period under consideration. The number of co-authors differs between fields, and indeed this is related to the steepness of the curves in Fig 2 . The steeper the curve, the less authors in the lower productivity groups have top cited papers, and one would expect this more in fields with less co-authors per paper. As Table 2 suggests, there is indeed negative relation between the average (and the median) number of co-authors, and the steepness of the curve in Fig 2 .

https://doi.org/10.1371/journal.pone.0166149.t002

(iii) The effect of fractional counted productivity on the number of high-cited papers?

We did the above type of analysis also using fractional counting of productivity. The patterns are the same, with correlations of .37 and .79 (Figs 9 and 10 ). But the correlations are about .10 to .20 lower than in the full counted model. Also here, the co-author phenomenon may influence the result: if the highest cited papers have more co-authors than the other papers, fractionalization reduces the scores of the more productive researchers more, and lowers the correlation coefficient. This is indeed the case, the 6.3% most productive authors have 53% of the full counted PPtop 1% cited papers, but they have 46.8% of the fractional counted PPtop1% cited papers. In any case, the most productive researchers are also here decisive.

https://doi.org/10.1371/journal.pone.0166149.g009

https://doi.org/10.1371/journal.pone.0166149.g010

(iv) The effect of field adjusted production counting?

As discussed above, productivity figures differ between fields, and it may therefore be useful to normalize productivity data to field specific averages. The relation between the number of CSS1 papers and the total field adjusted output is strong: the correlation is high with r = 0.80 ( Fig 11 ), and not much smaller than in the above where we did not use the field adjusted production (0.90, see Fig 8 ). These results suggest that the more papers someone publishes, the higher the number fairly good papers cited above the threshold of CSS1.

https://doi.org/10.1371/journal.pone.0166149.g011

We do the same for CCS3 papers as dependent variable, the much narrower defined top, and field-adjusted productivity as independent variable. If we only include natural and health/life sciences, the correlation is considerable (r = 0.58), and about equally large as without applying FAP ( Fig 6 ). However, if we include all fields in the FAP, the correlation lowers to 0.37 ( Fig 12 ). This may be due to the fact that in some of the other fields the highest productivity levels are almost empty and that in some of those fields, the most productive researchers have a lower share (not a lower number) in the high impact paper class. As discussed above, this may be because they serve other audiences than only direct peers.

https://doi.org/10.1371/journal.pone.0166149.g012

Conclusions

As the above results show, there is not only a strong correlation between productivity (number of papers) and impact (number of citations), that also holds for the production of high impact papers: the more papers, the more high impact papers. More specifically, for most fields there are constant or increasing marginal returns. In that sense, increased productivity of the research system is not a perverse effect of output oriented evaluation systems, but a positive development. It strongly increases the occurrence of breakthroughs and important inventions [ 16 ], as would be expected from a theoretical perspective on scientific creativity [ 13 ]. Also, we find that other recent work points in the same direction [ 18 ; 20 ]. The lively discussion [e.g. [ 9 ; 10 ] that there is a risk of confusing quality with quantity therefore lacks empirical support. As we deployed a series of methods, with results all pointing in the same direction, the findings are not an artefact of the selected method. The increasing popular policy that allows researchers to hand in only their five or so best publications seems in the light of these results counterproductive, as it disadvantages the most productive and best researchers.

The analysis also gives an indication of the output levels that one may strive at when selecting researchers for grants or jobs. To produce high impact papers, certain output levels seem to be required–of course at the same time dependent on which field is under study.

Future work in this research line will cover various extensions: Firstly, we plan to extend the analysis to some other countries, which of course requires large-scale disambiguation of author names. Secondly, we will in a next version control for number of co-authors, and for gender [ 30 ]. The former relates to the discussion about team size and excellence, the latter to the ongoing debate on gender bias and gendered differences in productivity. Thirdly, the aim is to concentrate on principle investigators, and remove the incidental co-authors with low numbers of publications, as they may seem to be high impact authors at the lower side of the performance distribution. This all should lead to a better insight in the relation between productivity and impact in the science system.

Supporting Information

S1 file. confidence intervals (95%) for the mean number / share of css3 papers per field and by productivity class..

https://doi.org/10.1371/journal.pone.0166149.s001

Acknowledgments

The authors acknowledge support from the ERC grant 610706 (the GendERC project), and the Riksbankens Jubileumsfond grant P12-1302:1. An earlier version of this paper was published in the 2015 proceedings of the ISSI conference [ 31 ]. We are also grateful to a reviewer, whose suggestions resulted in more precise conclusions.

Author Contributions

Conceptualization: US PB.
Data curation: US.
Formal analysis: PB.
Investigation: US PB.
Methodology: PB US.
Resources: US.
Writing – original draft: US PB.
1. de Solla Price DJ. Little Science, Big Science. N.Y: Columbia University Press, 1963.
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15. Sandström U. Myths about Laureates and early recognition (In Swedish: Myter om nobelpristagare och deras tidiga uppmärksamhet). Forskningspolitiska studier 1/2014:Available from: http://www.forskningspolitik.se . Cited 17 Nov 2016.
28. Whitley P. The Intellectual and Social Organization of the Sciences. Oxford University Press, 2nd edition 2000.
30. Sandström U, van den Besselaar P. High productivity and high impact: gender differences? Forthcoming.
31. Van den Besselaar P, Sandström U. Does quantity make a difference? In Salah, S Sugimoto, U (Eds.). Proc. ISSI 2015 conference, Istanbul, Part Al, pp 577–583.

Taking off quantities

Taking off quantities from drawings involves a quantity surveyor recording the quantities and descriptions of materials and labour required to prepare a bill of quantities or schedule of rates. Best practice for taking off quantities is contained in the New Rules of Measurement: Detailed measurement for building works (NRM2) compiled and published by the Royal Institution of Chartered Surveyors, (RICS).

Dimension paper or dimension sheet.

Traditionally taking off quantities has used dimension paper or dimension sheets. As illustrated below dimension paper is divided into a series of columns.

Reading from left to right these columns are referred to as;

The binding column The binding column for binding dim sheets together.

The timesing column The timesing column is used to enter multipliers when there is more than one of a particular quantity and item to be measured. In the first example below the dimension 1.20 x 1.20 has been timesed or multiplied by 16.

The dimension column The dimension column, where the measurements are recorded always in the order of; length, width, depth or height and to two decimal places.

The squaring column. The squaring column, where the calculated quantities are entered.

The description column.

The description column contains the description of the item to be priced. The terminology in taken from NRM2. Sometimes descriptions are abbreviated.

Note that dim paper has two independent columns per sheet and that the right-hand side of the dimension column is referred to as the ‘waste’.

Waste calculations (see top of column 2) The waste is anything but waste and contains the calculations behind the take-off dimensions to three decimal places.

Is used where two descriptions share the same dimensions.

Taking-off list

A very useful aid memoire for the taker-off and some abbreviations are used in the descriptions.

Taking off quantities for reinforced in-situ concrete

On the following dimension sheet similar techniques have been applied to taking-off quantities for formwork and reinforcement.

Increasingly taking off, which used to be a labour-intensive operation, is performed using specialised software packages, of which there are a number available. Software packages will enable a taker-off to enter dimensions and descriptions, the software will then collate and produce a bill of quantities. Even though technology has taken much of the repetition out of the measurement process, to use taking-off software it if still necessary to have sound taking-off and measurement skills.

For many years traditional measurement or dim paper has been used for taking off but increasingly where taking off is not carried using software, spreadsheets are used, although spreadsheets will not produce the finished bill of quantities.

Taking-off skills are not only used in the preparation of bills of quantities or work packages, but also through the entire life cycle of a construction project. For example;

To prepare estimates and cost plans,

To evaluate various design alternatives,

To estimate tender costs,

In the measurement of variations or change orders,

In calculating payments on account (stage payments) and

In preparing and agreeing the final accounts.

Taking off is not only used in the preparation of bills of quantities for building projects but also for large scale civil engineering works such as HS2. Civil engineering taking off uses its’ own set of rules known as the Institution of Civil Engineers Standard Method of Measurement 4 (CESMM4) and although the rules differ from NRM2 the process of taking off quantities remains the same.

Duncan Cartlidge Online gives 24/7 access to a series of clear video tutorials from the author of the best-selling pocketbooks. Each video goes through the taking off process stage by stage referring to the latest technologies and techniques, using both tradition and spreadsheet examples together with detailed interpretation of NRM2. Extensive experience both in practice and in education allows Duncan Cartlidge to address the common problems encountered when taking off quantities. Each video contains a set of self-assessment questions to gauge progress and a question and answer facility will be available to subscribers.

Measurement / taking-off content currently includes videos covering;

Introduction to taking-off

NRM2 explained

Bill of quantities documentation

Groundworks

In-situ concrete

First fix / flat roofs

Pitched roofs

Internal finishes

Mechanical installations

Electrical installations

New taking-off sections added regularly

Other measurement video tutorials include;

Taking-off using CESMM4

International Cost Measurement Standards (ICMS)

International Property Measurement Standards (IPMS)

In addition to taking-off quantities other sections include:

Estimating and

Project management

Cost advice

Contract administration

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Units of paper quantity
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For example, paper mills often quote in this unit to help compare apple to apple ($26.15/M for 50 lbs. paper vs. $30.22/M for 70 lbs. paper). This unit is also common in the online media industry where banner advertising or email marketing is sold at CPM (cost per thousand impressions). ... and your product line has an annual usage of 250,000 ...
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3 Types of Dimension Paper / Takeoff Sheets Used by Quantity Surveyors
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Quantity and/or Quality? The Importance of Publishing Many Papers
In this paper we will use two levels, level CSS1 and CSS3, which in the former case cover the 37% most cited papers, and in the latter case the about 3.5% of most cited papers: the "outstandingly cited papers" [ 24 ]. In the following we will investigate the relation between quality and quantity in several different ways.
Taking off quantities
Dimension paper or dimension sheet. Traditionally taking off quantities has used dimension paper or dimension sheets. As illustrated below dimension paper is divided into a series of columns. Reading from left to right these columns are referred to as; The binding column The binding column for binding dim sheets together. The timesing column
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1.3 The Language of Physics: Physical Quantities and Units

Teacher Support

Section Key Terms

The Role of Units

SI Units: Fundamental and Derived Units

The Kilogram

Metric Prefixes

Known Ranges of Length, Mass, and Time

Using Scientific Notation with Physical Measurements

Unit Conversion and Dimensional Analysis

Worked Example

Using Physics to Evaluate Promotional Materials

Accuracy, Precision and Significant Figures

Uncertainty

Percent Uncertainty

Calculating Percent Uncertainty: A Bag of Apples

Uncertainty in Calculations

Precision of Measuring Tools and Significant Figures

Significant Figures in Calculations

Significant Figures in this Text

Approximating Vast Numbers: a Trillion Dollars

Graphing in Physics

Analyzing a Graph Using Its Equation

Using Logarithmic Scales in Graphing

Method of Adding Percents: Shingling Your Roof

Virtual Physics

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Paper Quantities – Ream, Quire, Bundle, Bale & Pallet

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Paper Quantities – Ream, Quire, Bundle, Bale, Pallet and Other Quantities