write 0 00147 in standard form

Standard Form Calculator

Use this calculator to easily convert a number in standard form (a.k.a. scientific notation, a.k.a. engineering notation). Write a large number or a decimal with a many digits past the decimal point in standard form.

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• What is the standard form of a number?
• Writing a number in standard form

    What is the standard form of a number?

The standard form is also called E-notation , scientific form of a number, or standard index form . It is a way of expressing numbers deemed too large or too small to be conveniently written in the more familiar decimal form. Many calculators support scientific mode for working with such numbers. Even though it is less necessary now than in times before personal computing, the standard form remains popular among engineers, scientists and mathematicians, as well as students in these disciplines.

The form of a number in standard notation is m x 10 n which reads " m times 10 raised to the power of n ". The exponent n is always an integer (whole number) while the coefficient m (mantissa, significand) can be any real number. The most convenient form (normalized notation) is one in which the exponent is chosen in such a way that the coefficient is between 1 and 9. The sign of the number is written the usual way - with a plus or minus before it.

Writing numbers in standard form makes it easier to compare orders-of-magnitude. For example, the mass of a proton is 0.000 000 000 000 000 000 000 001 6726 g and the mass of an electron is 0.000 000 000 000 000 000 000 000 000 910 938 356 g. It is hard to compare the two this way, but when we write them as 1.6726 x 10 -24 and 9.109 383 56 x 10 -28 we can just compare the exponents, and since -24 is larger than -28, the proton is about 4 orders of magnitude (10,000 times) more massive than the electron.

    Writing a number in standard form

It should be noted that converting decimal numbers to standard form numbers does not change the value of the number, it just changes its form, as suggested by the name. Using our standard form calculator, you can do the conversion quickly and easily, however if you want to do it by hand, here is the algorithm for doing so.

• Move the decimal point enough places so that the number becomes smaller than 10, but larger than 1.
• If you moved the decimal point to the left, append "x 10 n " to the number, where n is the number of positions you moved the point. If you moved it to the right, append "x 10 -n ", using the same logic.

For example, let us write the number 12,340,000 in normalized standard form. First, we move the decimal point 7 positions to the left so the number becomes 1.2340000. We can drop the zeroes in most scenarios (unless we want to keep them as significant digits to indicate precision) so, after adding x 10 7 we can write it down as 1.234 x 10 7 in scientific notation and 1.055e7 or 1.055e+7 in e notation. Both types of notations are supplied when using our online tool.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Standard Form Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/standard-form-calculator.php URL [Accessed Date: 25 May, 2024].

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Standard Form Calculator

Use of standard form calculator.

You can calculate the real number, scientific notation, E-notation, and engineering notation through this calculator. To convert a number, follow the below steps.

• Enter the number in the input box.
• Click calculate
• The result will be shown in four different forms

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This standard form calculator is a tool that helps to express numbers in scientific notation. 

This calculator also provides other types of notations for numbers i.e

• Real Number
• E-number 
• Engineering notation

This standard form converter would provide you with the correct results. It is an option that does not involve the hassle of writing down the solution steps and then getting to the answer.

What is the standard form?

A Simple definition of standard form is:

"It is a method of expressing numbers as a power of ten" .

This method of writing numbers was devised by scientists for convenience in reading and calculations. Scientific notation is another term for standard form.

Standard form format:

The general format in which we write numbers to represent them in standard form is:

\(a \times b^{10}\)

Here, “a” is some number that is greater than or equal to 1 and is smaller than 10. While “b” is the number that is the power of 10. we will get the original number if we multiply a with the solved value of \( b^{10} \)

How to write in standard form?

To convert a number to the standard form, it is important to understand the process properly in a stepwise manner. Below, the steps are explained through an example.

Convert 678120009 into standard form.

• Place the decimal point   6.78120009
• Count the digits after the decimal place.  There are 8 digits after the decimal.
• Raise this number to the power of 10 and multiply it to the original value. \(6.78120009\: \times 10^8\)
• Round up to the third-place value. \(6.78\: \times 10^8\)

Negative exponents:

Decimal numbers have small values. Hence, when you are converting them to standard form, the power of ten is negative. Similarly, when you are converting a large number to a standard form (scientific notation), the power of ten would be positive.

An example of a standard form with a negative exponent is:

\(0.000678 = 6.78 \times 10^{\left(-4\right)}\)

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Standard Form Calculator

Convert a number to standard form by entering the decimal value below. You can also convert a number in standard form to decimal.

Hint: use a format such as 5.2 × 10^8 to represent standard form.

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How to write a number in standard form, how to express a small number in standard form, how to write precise decimals in standard form, how to use standard form in equations, frequently asked questions.

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Standard form , also referred to as scientific notation , is a way of representing very large numbers or very small numbers in a concise format that is easier to read.

Numbers in standard form are written as an expression of a coefficient multiplied by 10 to the nth power.

For instance, the number 25,970,000 can be expressed using standard form as 2.597 × 10 7 .

The number of digits in the expression’s coefficient will vary depending on the number of significant figures in the number. You can use a sig fig calculator to find the significant figures.

You can convert a number from decimal to standard form in a few simple steps.

Step One: Create the Equation

First, create an expression with the initial number in decimal form as the coefficient multiplied by 10 to the power of 0 (recall 10 0 = 1).

For example, let’s create the initial standard form equation for the decimal 25,970,000. 25,970,000 = 25,970,000 × 10 0

Step Two: Move the Decimal Point

The next step is to move the decimal point in the coefficient until there is one significant digit to the left of the decimal point. For small numbers less than 1, you would move the decimal point to the right.

For each space the decimal point is moved to the left, increase the 10’s exponent by 1. For numbers less than 1, reduce the exponent by 1 for each space the decimal point is moved to the right.

Continuing the example above, let’s finish converting 25,970,000 to standard form.

25,970,000 = 25,970,000.0 × 10 0 25,970,000 = 2,597,000.0 × 10 1 25,970,000 = 259,700.0 × 10 2 25,970,000 = 25,970.0 × 10 3 25,970,000 = 2,597.0 × 10 4 25,970,000 = 259.7 × 10 5 25,970,000 = 25.97 × 10 6 25,970,000 = 2.597 × 10 7

You can use our exponent calculator to learn more about working with exponents in a standard form equation.

You can also represent small numbers, much less than one, in standard form as well. The main difference is instead of moving the decimal point to the left, you move it to the right, and instead of increasing the 10’s exponent, you decrease it.

For example, let’s express the number 0.00000659 in standard form:

0.00000659 = 0.00000659 × 10 0 0.00000659 = 0.0000659 × 10 -1 0.00000659 = 0.000659 × 10 -2 0.00000659 = 0.00659 × 10 -3 0.00000659 = 0.0659 × 10 -4 0.00000659 = 0.659 × 10 -5 0.00000659 = 6.59 × 10 -6

What if you have a long, precise decimal? How do you write that in standard form? The standard practice is to write the standard form coefficient with the same number of significant figures as the decimal.

For example, the number 72,001,000 has five significant figures and can be written in standard form as 7.2001 × 10 7 .

Another example of a very precise decimal is 8,756,992.34 (with nine sig figs) and can be written in standard form as 8.75699234 × 10 6 . You may notice that in the latter example, it does not seem much simpler to write the decimal in standard form.

In practice, if one is dealing with very precise numbers like these, it is best to either leave them in decimal form or round them to a few significant figures , purely for the purpose of simpler viewing. For example, you may round 8.75699234 × 10 7 to 8.76 × 10 7 .

However, it is very important to remember that when actually performing calculations, you must use the full decimal or standard form, not the rounded value.

When dealing with very large or very small numbers in equations, it is often beneficial to rewrite these values using standard form. For example, you can write an equation of a line such as y = 5600000x + 820000000 , but this is not ideal to read.

Instead, you can rewrite these values into standard form:

y = 5.6 × 10 6 x + 8.2 × 10 8

Although this is much cleaner, do you notice the problem? By writing the numbers in standard form, we have introduced multiplication signs that can be confused for the variable x .

Therefore, when using standard form in equations, we can use a different practice commonly used in mathematics. That is, replace the multiplication sign and the 10 with the letter e .

As an example, 1.12 × 10 9 can be rewritten as 1.12e9.

To help you remember this simpler form, think of e as standing for “exponent”.

Continuing our example from above, we can rewrite y = 5.6 × 10 6 x + 8.2 × 10 8 as y = 5.6e6x + 8.2e8 , and the confusion between the multiplication sign and the variable x disappears!

Why do we use standard form?

We use standard form because equations and calculations with very large or very small values become unwieldy and cumbersome. Also, by removing the leading or trailing zeros, all the numbers left in the coefficient are significant.

Are standard form and scientific notation the same thing?

Yes, standard form and scientific notation are different names for the same format.

Can negative numbers be written in standard form?

Absolutely! Negative numbers can be written in standard form in the exact same way as positive numbers. For example, -0.0045 can be written as -4.5 × 10 -3 or -4.5e-3.

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Standard Form Calculator

To Find Standard form you can enter values as Following

• Standard Version: 2000.02 x 10^2
• UK Version: 2000.02

Real Number :

Scientific notation :, e-notation :, engineering notation :, other calculators, standard form calculator.

The standard form converter   converts the given number to:

• Scientific notation
• Real number
• E-Notation, and
• Engineering notation

A standard notation converter accepts values both in exponential and decimal form and converts the input to standard notation in a heartbeat.

Keep on reading if you are interested in the standard form definition, how to find standard form   manually, and a few examples of standard or scientific notation.

How does this standard notation calculator work?

To convert numbers into the standard form follow the steps below:

• Enter the decimal or exponent number in the input box.
• Click the " Convert" button.
• The standard form calculator will convert the number into four different notations.
• Click the " reset " button if you want to recalculate.

After pressing the convert button this standard form calculator will convert your decimal or exponent number into the standard form and also gives the result in real numbers, scientific notation, E notation, and Engineering notation.

What is the standard form?

Standard Form is a term in mathematics that is used for converting long or complex numbers into the simplest form for reducing the difficulty to read the number.

It is a way to express very small or very long numbers.

The scientific notation calculator can be used for converting complex numbers into a readable format.

A large mathematical number like the given below is difficult to read. But, after it is converted into the standard form, it becomes easier to read.

Number: 5630000000000

Standard Form: 5.63 x 10 12

Here is an example of the conversion of small numbers into the standard form:

Number: 0.0000067833

Standard Form: 6.7833 -6

How to write in the standard form manually?

Below, we have explained the step-by-step conversion of a number into the standard format.

Convert 0.000381 to standard form.

Step 1:  Write down the number.

Step 2:  Find the  decimal point  in the number and if the decimal point is not there then it would be declared at the end of the number, on the right side.

Step 3:  Place the decimal after the first non-zero digit and remove any leading or trailing zeros. In this case:

The number becomes,

Step 4:  Now, count the number of positions you have changed for the decimal. Raise the total number of positions moved, to the power of 10. In this case, we have moved the decimal to 4 positions.

Keynote: If the decimal is moved from left to right, place the negative sign with the exponent . If the decimal is moved from right to left, raise the power as a positive integer

0.000381 = 3.81 × 10 -4

Use the standard notation calculator to cross-check the answers.

What is the standard form of a Million?

The standard form of 1 million is 1 x 10 6 .

What is Standard Fraction?

The Standard Form of the fractions is known as the Standard Fraction. When the numerator and denominator are co-prime then it is considered to be written in the standard form. But for this, both the numbers shouldn’t have a common factor of 1 For example. 5/6, 11/12.

What is the standard form of the quadratic function?

The general way of writing the quadratic function is:

f(x) = ax 2 + bx + c

In Standard form, it is written as:

f(x) = a(x-h) 2 + k

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Standard Form Calculator

Type or paste the number in the standard notation calculator and click Calculate to convert the numbers into the standard form.

Table of Contents:

What is Standard form?

How to write in standard form.

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Standard form calculator converts long and small numbers into standard scientific form. This standard form converter gives the result in the following forms.

• Real Number
• Scientific notation
• Engineering notation

Standard form is a way of writing down very large or very small numbers easily. Using scientific or standard notation, we can easily interpret these numbers and use them in equations or experiments, etc.

Convert 85400000067 in standard form step-by-step.

Step 1: Place the decimal after the first non-zero digit.

= 8.5400000067

Step 2: Count the digits after the decimal and raise it as the power of 10.

 = 10 10

Step 3: Round off  the 2nd place digit after the decimal and multiply the value of 10 found in the second step.

= 8.54 × 10 10                  

The round-off step can be skipped if needed. In that case, the number in 1 st step is multiplied by a power of ten i.e. 8.5400000067 × 10 10 .

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Standard Form Calculator

Enter the number in the input box to write in standard form/Scientific E-Notation/Engineering Notation using our standard form calculator (converter)/standard notation.

Table of Contents:

How to use a standard form calculator?

What is standard form, how to write in standard form.

Is This Tool Helpful?

Standard form calculator is used to convert the numbers into standard form by placing the decimal value in the number. It converts a long number into an easily readable standard form.

To use this standard notation calculator , follow the below steps:

• Enter the number in the given input box.
• Press the Calculate button to see the result.
• You can reset the values by using the Reset

This standard form equation calculator will instantly show you the converted standard form of the given number. You can also use our scientific notation calculator and scientific notation converter to calculate the scientific notations.

If you are wondering what is a standard form in math , you are at the right place.

Standard form is used to reduce the difficulty in reading very large or very small numbers. The standard form of a number is any number between 1.0 and 10.0 multiplied by power 10, For example, 1.2× 10 2

For a demonstration of standard form, take a look at the below examples:

Number: 85500000000000

Standard form: 8.55 × 10 13

Number: 0.000458912

Standard form: 4.58 × 10 -4

You can use our standard form calculator to calculate the standard form of any number. However, we will explain how to convert a number to a standard form manually. To convert a number to standard form, follow the below steps:

• Write down the number .
• Identify the decimal point in the number. If there is no decimal point in the given number, it is considered at the right side of the number after the last digit.
• After identifying the decimal point, move the decimal to the first non-zero digit in the number.

• Count the total number of digits you have moved to the decimal point. Multiply the number by  10 and raise the power of 10 with the total number of digits the decimal has moved. If the decimal is moved from right to left, power will be positive , and if the decimal is moved from left to right, power will be negative .

Convert 0.0009 to the standard form.

Follow the steps to find the standard form of the given number.

Step 1 : Write down the number.

Step 2 : Identify the decimal point in the number. You can see the decimal point is lying after 4 digits from the left side.

Step 3 : After identifying the decimal point, move the decimal to the first non-zero digit in the number.

It will become 9. Because there is no non-zero digit after 9, we don’t need to write the decimal point after 9.

Step 4 : Count the total number of digits you have moved to the decimal point.

We have moved the decimal  4 places further. Multiply the number by 10 and raise the power of 10 with the total number of digits the decimal has moved. As we have moved the decimal point from left to right, the power will be negative .

9 × 10 -4

So, the standard form of the number 0.0009 is 9 × 10 -4 .

References: 

• Mathsisfun.com. Standard Form .
•   Splashlearn.com . What Is Standard Form? - Definition, Facts & Example.
•   Amathsdictionaryforkids.com . Standard Form ~ Reference By Jenny Eather.
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Standard Form Calculator

Table of content.

This standard form calculator allows you to convert numbers, equations, and general forms to standard forms or scientific notations by placing a decimal value in the number. It converts long numbers into an easily readable standard form. 

What is Standard Form in Math?

“The standard form math is the simplest form of a decimal number to enable them to read and write”. 

Oftentimes, reading and writing large numbers seems a daunting challenge, but to manage them by comparing the power of ten we use a standard form calculator. This calculator gives the result in the following forms.

• Scientific Notation
• Real Number
• Engineering Notation

What is standard notation of the number 0.00010? 

1 × 10^-4

A Method to Write a Number in Standard Form:

The standard form is also known as scientific notation where the given number is indicated as the decimal number times a power of 10. It can be very easy to write if we take into service the standard form calculator. It is written as:

a x 10^b 

Where: 

• a is the whole number which is 1≤|a|<10
• b is the integer that has a power of 10 

Rules For Standard Form:

A standard form is a writing style of equations, numbers, or expressions using a certain set of rules that are as follows:

• Standard form always uses the base 10 
• The number you multiply by the 10^n must in between 1.0 to 10.0
• The power to base 10 (n) must always be a whole number 

Steps to Convert a Number in Standard Form:

The below points are considered to be important when you want to convert a large or simple value into the standard form. So look at these. 

• Write a number and identify a decimal point . 
• If there is no decimal point then put it after the last number from the right side 
• After identifying the decimal, move the decimal to the first non-zero digit 
• Count the total number of digits that you have moved to a decimal point. 
• Multiply the counted number by the same power of 10 and remove a decimal. If the decimal moves from right to left power will be positive and If the decimal moves from left to right then the power will be negative. 

Practical Examples:

Suppose a complex term (7892374) which needs to convert to standard form.

In this value, there is no decimal according to the second above given step put the decimal after the last number from the right side. 

Move the decimal to the first nonzero digit 

7.892374 x 10^6

Working of Standard Form Calculator:

This online standard notation calculator functions well and simplifies your queries within a second when you put the below value in it. 

• Put the number into the designated field 
• Tap on “Calculate”
• Standard form of a given number
• Real number

Standard Form Table:

References: .

From the source Khan Academy: Standard form review, Converting to standard form , Finding features and graphs from the standard equation, 

From the source Wikipedia: Standard form .

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Standard Notation Calculator

What is standard notation, how to convert scientific notation into standard form, how to use standard notation calculator, our other useful tools.

Our standard notation calculator was created to instantly convert any number in decimal form or scientific notation to standard notation . Keep reading to learn more about what standard notation is , examples of standard notation, and how to write a chosen number in this notation .

Standard notation (or standard form ) means that values are displayed with commas every three positions and with a period as a decimal point, e.g., 5,786.04. The number has a regular place-value form with no multiplication sign or exponents. The value of each digit depends on which place it occupies. For example, 2 in 2,698 has a value of 2 thousand, while 3 in 3,412,000 is 3 million. You can easily multiply and divide numbers in standard notation by multiples of 10 :

• To multiply a number by a power of 10, move the comma to the right by the same number of places as the exponent (this will increase your number).

For example, 780 × 100 = 78,000.

• To divide a number by a power of 10, move the decimal to the left by the same number of places as the exponent (this will reduce your number).

For example, 0.08 / 1,000 = 0.00008.

Using scientific notation is convenient for very large or very small numbers. Scientific notation has two parts : the first is a number with a value from 1 to 10, and the second is the corresponding power of 10 , such as 2.7 × 10⁴ . If you want to convert scientific notation to the standard form :

• Find the exponent in the power of ten, e.g., 4 in 10⁴ .
• Move the decimal that many places to the right if the exponent is positive and to the left if the exponent is negative . Let's move the decimal four places to the right .
• Write zeros in the remaining blank spaces. Thus, 2.7 × 10⁴ in standard notation is 27,000 .

This standard notation calculator needs only three steps to convert to standard notation :

• Enter your number in decimal form, with an exponent (e), or in scientific notation. Let us enter the number 4450.
• Use "Advanced Mode" to modify significant numbers . This will give you the digits in a number that determine its accuracy. The default value is set to 10.
• Read the result with the standard notation calculator: 4,450.

We have a collection of other tools for writing numbers in different notations ; you can find them below:

• Scientific notation calculator ;
• Exponential notation calculator ;
• Scientific notation converter ;
• Scientific notation equation calculator ; and
• Engineering notation calculator .

What is the standard notation of 3.52 x 10⁷?

35,200,000 . To convert a number from scientific notation into the standard form:

• Identify the exponent in 3.52 x 10⁷; its value is 7 .
• Move the decimal point 7 places to the right .
• Fill in the five empty spaces with zeros.

What is the standard notation of 1.52 x 10⁻⁵?

0.0000152 . To convert to standard notation:

• Identify the exponent in the power of 10; it is -5 .
• Move the decimal point 5 places to the left .
• Fill in the four empty spaces with zeros.
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0.00147 in scientific notation

How to write 0.00147 in scientific notation? The scientific notation for decimal number 0.00147 is written as: 1.47 × 10 -3 .

Here we will show you how to convert decimal number 0.00147 to scientific notation with step by step detailed solution.

First note that all the numbers in scientific notation are written in the form m × 10 n , where n is an integer and the coefficient m is a non-zero real number between 1 and 10 in absolute value.

To convert 0.00147 into scientific notation also known as standard form, follow these steps:

• Move the decimal 3 times to right in the number so that the resulting number, m = 1.47, is greater than or equal to 1 but less than 10
• Since we moved the decimal to the right the exponent n is negative n = -3
• Write in the scientific notation form, m × 10 n = 1.47 × 10 -3

Therefore, 0.00147 in scientific notation is written as 1.47 × 10 -3

Here are some more examples of decimal form to scientific notation conversion

• 0.00148 in scientific notation
• 0.00149 in scientific notation
• 0.00150 in scientific notation
• 0.00151 in scientific notation
• 0.00152 in scientific notation
• 0.00153 in scientific notation
• 0.00154 in scientific notation
• 0.00155 in scientific notation
• 0.00156 in scientific notation

Standard Form

What is "Standard Form"?

that depends on what you are dealing with!

I have gathered some common "Standard Form"s here for you..

Note: Standard Form is not the "correct form", just a handy agreed-upon style. You may find some other form to be more useful.

Standard Form of a Decimal Number

In Britain this is another name for Scientific Notation , where you write down a number this way:

In other countries it means "not in expanded form" (see Composing and Decomposing Numbers ):

Standard Form of an Equation

The "Standard Form" of an equation is:

(some expression) = 0

In other words, "= 0" is on the right, and everything else is on the left.

Example: Put x 2 = 7 into Standard Form

x 2 − 7 = 0

Standard Form of a Polynomial

The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first (like the "2" in x 2 if there is one variable).

Example: Put this in Standard Form:

3 x 2 − 7 + 4 x 3 + x 6.

The highest degree is 6, so that goes first, then 3, 2 and then the constant last:

x 6 + 4 x 3 + 3 x 2 − 7

Also, within each term, it is nice to have the variables in alphabetical order (if it does not make things more confusing):

yzx 2 + 4 yx 3

The highest degree is 3, so that goes first, also put the variables in alphabetical order

4 x 3 y + 3 x 2 yz

Standard Form of a Linear Equation

The "Standard Form" for writing down a Linear Equation is

Ax + By = C

A shouldn't be negative, A and B shouldn't both be zero, and A , B and C should be integers.

Bring 3x to the left:

−3x + y = 2

Multiply all by −1:

3x − y = −2

Note: A = 3, B = −1, C = −2

Ax + By + C = 0

is sometimes called "Standard Form", but is more properly called the "General Form".

Standard Form of a Quadratic Equation

The "Standard Form" for writing down a Quadratic Equation is

( a not equal to zero)

Expand "x(x−1)":

x 2 − x = 3

Bring 3 to left:

x 2 − x − 3 = 0

Note: a = 1, b = −1, c = −3

Standard Form of a Circle Equation

With a circle like this:

The Standard Form is this:

(x−a) 2 + (y−b) 2 = r 2

See Circle Equations for more details.

Write 0.00147 in standard form.

Gauth ai solution.

Standard Form

Learn about standard form., standard form lesson, definition of standard form.

Standard form is the standard way of writing something. In mathematics, there are many different standard forms. For example, there is a standard form for writing a number, an equation, a polynomial, and so forth.

We will go through the most common algebraic standard forms in this lesson.

Standard Form of a Number

Writing numbers in standard form is also known as scientific notation. The form is given as:

Where C is a decimal number between 0 and 10, such as 6.35. C is shown with two decimal places in the following example. However, we can write out as many decimal places as necessary.

Example problem:

Write the number 36,500 in standard form, also known as scientific notation.

• Let's move the decimal to the left 4 places so that C = 3.65. C will need to be multiplied by 10 4 to equal 36,500.
• The number is written in standard form as 3.65 x 10 4 .

Standard Form of a Polynomial

A polynomial is in standard form if the terms' exponents are in descending order. In other words, the term with the highest power should be furthest to the left and the term with the lowest power should be furthest to the right.

Rewrite the polynomial 3x 2 + x - 2x 3 + 6 in standard form.

• Let's rearrange the terms so that the exponents are in descending order.
• 3x 2 + x - 2x 3 + 6 → -2x 3 + 3x 2 + x + 6
• The polynomial is rewritten in standard form as -2x 3 + 3x 2 + x + 6.

Standard Form of an Equation

An equation is in standard form if it is set equal to zero. For example, the equation 4y 3 + y = 5 can be rearranged to standard form by moving the 5 to the left side of the equals sign. Standard form of this equation is 4y 3 + y - 5 = 0.

Standard Form of a Linear Equation

The standard form of a linear equation is given as:

Ax + By = C

Where A , B , and C are constants, and x and y are variables. This standard form is only applicable for the equation of a line.

Rewrite the equation y = 4x + 2 in standard form.

• The equation is currently in slope intercept form. Let's move the term 4x over to the left side of the equals sign.
• y = 4x + 2 → -4x + y = 2
• The linear equation is written as -4x + y = 2 in standard form.

Standard Form of a Quadratic Equation

The standard form of a quadratic equation is given as:

ax 2 + bx + c = 0

Where a , b , and c , are constants, and x is a variable.

Rewrite the quadratic -4x - 12 = 2x 2 in standard form.

• We must have all nonzero terms on one side of the equals, and the zero term on the other side of the equals. The nonzero terms must also be in descending order of exponent power.
• -4x - 12 = 2x 2 → 2x 2 + 4x + 12 = 0
• The quadratic is written as 2x 2 + 4x + 12 = 0 in standard form.

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RadfordMathematics.com

Online mathematics book, search radford mathematics, standard form - part 1, (how to write a number in standard form).

The idea behind standard form is to write both very large and very small numbers in a convenient form. Here are a couple of examples of numbers written in standard form :

• the distance from the Earth to the Sun is: \(149\ 600 \ 000 \ 000 \) m. In standard form this is written \(1.49 \times 10^{11}\) m.
• The size of a Molecule of Oxygen is: \(0.000000000152\) m. In standard form this is written \(1.52 \times 10^{-10}\) m.

Tutorial 1: Writing Numbers in Standard Form

In this tutorial we learn how to write numbers in standard form . We do so by writing the three numbers:

• \(273\ 000\ 000\)
• \(0.0000273\)

Standard Form

When we write a number in standard form , we must write it in yje following way: \[a \times 10^k\] where the following two conditions must be met:

• \(1 \leq a < 10\), the number \(a\) must be greater than, or equal to, \(1\) and must be less than \(10\).
• \(k\in \mathbb{Z}\), in other words the power on \(10\) must be an integer: \(\mathbb{Z} = \left \{ \dots , -3, \ -2, \ -1, \ 0, \ 1, \ 2, \ 3, \ \dots \right \}\)

Write each of the following numbers in standard form :

• \(3,240,000 \)
• \(0.0000123\)
• \(137,000\)
• \(607,000,000,000\)
• \(0.000000103\)
• \(0.00089\)

Solution Without Working

We find the following results:

• \(3,240,000 = 3.24 \times 10^6\)
• \(0.0000123 = 1.23 \times 10^{-5}\)
• \(137,000 = 1.37 \times 10^5\)
• \(0.0074 = 7.4 \times 10^{-3}\)
• \(607,000,000,000 = 6.07 \times 1O^{11}\)
• \(0.000000103 = 1.03 \times 10^{-7}\)
• \(9 = 9\times 10^0 \)
• \(0.67 = 6.7\times 10^{-1}\)
• \(43,000 = 4.3\times 10^4\)
• \(0.00089 = 8.9 \times 10^{-4}\)

Answers with Working

Select the question number you'd like to see the working for:

Rounding & Standard Form

When writing numbers in standard form, we usually round numbers to two or three significant figures . For instance, consider the number: \[2 \ 347 \ 128\] Without any rounding , writing this in standard form , leads to: \[2.347128\times 10^6\] This notation isn't practical. Instead, when writing numbers in standard form, we usually round to 2 or 3 significant figures, so that \(2.347128\times 10^6\) becomes:

• \(2.3\times 10^6\) to two significant figures (2 sf)
• \(2.35\times 10^6\) to three significant figures (3 sf)

Writing all of your answers to three significant figures , write each of the following in standard form :

• \(278,120,001\)
• \(0.0004352617\)
• \(31,906,321,003\)
• \(0.000000789654\)
• \(301,888 \)
• \(0.010345\)
• \(978,909,456,001,745\)
• \(0.0050216\)
• \(0.435269\)
• \(278,120,001 = 2.78 \times 10^6\)
• \(0.0004352617 = 4.35 \times 10^{-4}\)
• \(31,906,321,003 = 3.19\times 10^9\)
• \(0.000000789654 = 7.90 \times 10^{-7}\)
• \(301,888 =3.02 \times 10^5\)
• \(0.010345 = 1.03\times 10^{-2}\)
• \(978,909,456,001,745 = 9.79 \times 10^{14}\)
• \(0.0050216 = 5.02\times 10^{-3}\)
• \(8,927 = 8.93\times 10^3 \)
• \(0.435269 = 4.35\times 10^{-1}\)

Standard Form & Calculators

Although some calculators can present results in standard form, many use a slightly different notation to the one we have see here.

Calculators replace the number \(10\) by the letter \(E\)

Here are some examples of what a calculator can display and the number, in standard form , they are referring to.

With your calculator, try calculating: \[987,654,321 \times 123,456,789\] You're likely to find: \[1.21933\text{E}17\] This means: \[1.21933\times 10^{17}\]

Notice that we had to convert the number in decimal form, via:

With your calculator, try calculating: \[5 \div 1234567890\] You're likely to see a result looking like: \[4.05\text{E}-9\] This means: \[4.05\times 10^{-9}\]

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How to Write Numbers in Standard Form

Last Updated: February 17, 2023 Fact Checked

This article was reviewed by Grace Imson, MA . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. There are 8 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 159,969 times.

Standard form, also known as scientific notation in the US, is a method of expressing very large or very small numbers. It's used in science and math as shorthand, rather than writing out the full number every time you use it. This form also makes doing calculations much easier than working with a number that could have multiple place values. If you handle numbers with many digits, either very large or very small ones, then converting them to standard form by following this process will help.

Writing Large Numbers

• If the original number was 1,500,000, then write it was 1,500,000.0.
• If the number is already a decimal, like 1,200,000.325, skip this step. For the next step, count from the decimal point that’s already there.

• Since the original number is 1,500,000.0, count until you reach the 1. There are 6 place values between the decimal point and the 1.
• Remember the amount of values you counted. This is important later on.
• This also works without zeroes. For 657,799,596.0, there are 8 place values between the decimal point and the 6.
• The first few place values are ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions. The place values continue rising as numbers get bigger.

• The number 1,500,000.0 changes to 1.500000.
• Do the same action if the second digit is a zero. For instance, 5,000,000 becomes 5.000000.
• If the decimal point was printed on the page and you can’t erase it, put a line through it so you remember it’s been moved.

• After eliminating the extra zeros, 1.500000 becomes 1.5.
• Only get rid of zeros at the end of the number. If the number is 8.100200, only get rid of the last 2 zeros so the number is 8.1002.

• Since there are 6 place values between the decimal points in 1.5 (1,500,000), the exponent is 10 6 .
• In standard form, the number with an exponent is always 10, never a different number.

• For the original number, 1,500,000, the standard form is 1.5 x 10 6 .

Expressing Very Small Numbers

• If the original number is 0.000325, count the place values between the decimal point and the 3. There are 4 spaces.
• There shouldn’t be zeros at the end of a decimal. If there are, erase or cross them out before counting the spaces.

• If the original number is 0.000325, move the decimal point and eliminate the zeros so it’s 3.25.
• If there are zeros between 2 non-zero digits, keep them. For .034002, write 3.4002.

• If the original number was 0.000325 and there are 4 spaces between the decimal points, write 10 4 .

• The original exponent, 10 4 , becomes 10 -4 .

• For the final result, 0.000325 becomes 3.25 x 10 -4 in standard form.

Converting Numbers from Written Form

• If a number is spelled out as six hundred and thirty-seven thousand, four hundred ninety-two, start at the left. The first part is six hundred and thirty-seven thousand. Write this as 637,000. The second part is four hundred, so write 400. The final part is ninety-two, so write 92.
• You can do the same with small numbers as well. Very small numbers are common in measurements, like "one-thousandth of an inch." The thousands place value is 4 spaces to the right of the decimal point. So in written form, this is 0.0001.
• Another way to convert small numbers is to imagine them as fractions. "One-thousandth of an inch" is equal to 1/1,000. Divide 1 by 1,000 and get 0.0001.

• For our example, your equation is 637,000 + 400 + 92. The result of the equation is 637,492.
• If you're in the US, remember to add a comma after every 3 digits starting from the left to keep track of the number. If you end up with 545600, for example, make it 545,600.
• Outside the US, use decimal points instead of commas. So 545,600 should be 545.600.

• For 637,000, going through the process gives you 6.37 x 10 5 .
• Do the same with small numbers as well. If one-thousandth of an inch is 0.0001, then convert it to standard form by going through the process to write small numbers. The result is 1 x 10 -4 .

Community Q&A

You Might Also Like

• ↑ https://youtu.be/ceneATH5EZ8?t=65
• ↑ https://www.mathsisfun.com/algebra/standard-form.html
• ↑ https://youtu.be/ceneATH5EZ8?t=35
• ↑ https://sciencing.com/write-numbers-standard-form-6561983.html
• ↑ https://revisionmaths.com/gcse-maths-revision/number/standard-form
• ↑ https://youtu.be/wd4cRAoBOiE?t=71
• ↑ https://youtu.be/wd4cRAoBOiE?t=178
• ↑ https://www.mathsisfun.com/definitions/standard-form-numbers-.html

About This Article

To write numbers in standard form, add the numbers in expanded form together in order to get the result. For example, if the expanded number is 3,000 + 500 + 20 + 9 + 0.8 + 0.01, you would add up all those numbers to get the standard form, which is 3,529.81. For numbers in written form, convert the words into numbers, such as by changing seven-thousand nine-hundred forty-three to 7,943. For tips on how to use British standard form and how to use standard form for complex numbers, read on! Did this summary help you? Yes No

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• Decimal Numbers Standard Form

Standard Form a Number in Maths

Decimal numbers in standard form are the simplest form, that can be easily read and written. For example, the standard form of decimal number 0.007 is 7 × 10 -3 . Sometimes it is very difficult to read or write very large or very small numbers . Hence, we write them in standard form. Not only decimals but any number can be written in standard form. In this article, we are going to learn what is the standard form of a number, how to express decimal numbers in standard form with many solved examples in detail.

What is the Standard Form of a Number?

A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.

The correct definition of standard form could be explained better in terms of decimal numbers and following certain rules.  As we know, decimal numbers are the simplified form of fractions.

Some fractions give decimal numbers which have numbers after decimal at thousandths, hundredths or tenths place. But there are some fractions, which give a big decimal number. To represent such big numbers, we use simpler forms, which are also stated as Scientific notation.

Basically, we can say, it is the representation of rational numbers in standard form. Rational numbers are numbers that can be represented in the form of p/q, where p and q are both integers. For example, 1/10, 4/5, 8/9, etc.

How to Write the Standard Form of a Number?

The steps to write the standard form of a number are as follows:

Step 1: Write the first number from the given number.

Step 2: Add the decimal point after the first number.

Step 3: Now, count the number of digits after the first number from the given number and write it in the power of 10.

For example, 52300000000 is the number. Thus the standard form of a number is obtained as follows:

Step 1: The first number is 5

Step 2: Adding the decimal point after 5, it becomes “5.”

Step 3: The number of digits after 5 is 10.

Hence, the standard form of 52300000000 is 5.23× 10 10 .

How to Write Decimal Numbers in Standard Form?

Decimal numbers employ 10 as the base and require 10 different numerals and a dot for the representation of its numbers. In this system, the digits used in denoting the number take different place values depending upon their position. For example, the number 645.221 can be written as 6 hundreds 4 tens 5 ones 2 tenths 2 hundredth and 1 thousandth.

Now, let us discuss how to write the decimal numbers in standard form.

Step 1: Write the first non-zero digit from the given number

Step 2: Add the decimal point after the first non-zero digit

Step 3: Find the number of the decimal point that shifts from the given number and write it to the power of 10.

For example, 0.0000017 in standard form is as follows:

Step 1: In the given number, the first non-zero digit is 1

Step 2: Add decimal point after the number 1. Hence, it becomes “1.”

Step 3:  Here, the decimal point shifts 6 places to the right.

Hence, the standard form of a number 0.0000017 is 1.7 ×10 -6

In this section, we shall learn about the representation of numbers in the expanded form.

Numbers in Expanded Form

Let us consider a 6 digit number 657891. In the expanded form this number can be written as:

657891 = 6 × 100000 + 5 × 10000 + 7 × 1000 + 8 × 100 + 9 × 10 + 1

We can express this number in the exponential form as well, as we know that 10000=10 4 , 10 = 10 0  and so on.

657891 = 6 × 10 5 + 5 × 10 4 + 7 × 10 3 + 8 × 10 2 + 9 × 10 1 + 1 × 10 0

Expanded Form of Decimal Numbers

Similar to whole numbers, we can write the decimal numbers in expanded form, also. To decimal into expanded form, we need to multiply digits with increasing exponents of 1/10 or 10 -1 .

Let us understand with the help of an example.

Example: Write 0.986 in expanded form.

0.986 = 9 × 10 -1 + 8 × 10 -2 + 6 × 10 -3

= 9 × 1/10 + 8 × 1/100 + 6 × 1/1000

= 0.9 + 0.08 + 0.006

Standard Form of a Rational Number

A rational number ‘p/q’ is said to be in the standard form if the denominator q is positive and both the integers a and b have no common divisor other than 1.

Steps to convert a rational number into the standard form:

• Write the given rational number.
• Check if the denominator is positive or negative. If it is negative, then we need to multiply both numerator and denominator by -1, to make the denominator positive.
• Now, find out the greatest common divisor (GCD) of numerator and denominator, which could be cancelled.
• Divide the numerator and denominator by GCD.
• The obtained number is the Standard form of the given rational number.

How to Express Large Numbers in Standard Form?

Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of representation is termed as the standard form. We can understand this concept with the following examples.

500 = 5 × 10 2

567 = 5.67 × 10 2

56.78 = 5.678 × 10 1

The advancement in science and technology has introduced us to numbers as big as the diameter of the Earth and as small as the size of a human cell. In order to represent these numbers, we use the exponential form to make their reading and writing more convenient.

Video Lesson on Numbers

Related Articles

Solved examples.

Example 1: Represent 567.21 in exponential form.

567.21 = (5 × 100) + (6 × 10) + 7 + (2 × 1/10) + (1 × 1/100)

Writing it in the exponential form:

567.21 = 5 × 10 2 + 6 × 10 1 + 7 × 10 0 + 2 × 10 -1 + 1 × 10 -2

Example 2 : Represent the distance between the Earth and the Sun in exponential form.

Solution: The distance of the Earth from the Sun is 1496000000 km.

1496000000Km = 1.496 × 10 9 Km

Example 3 : Express the size of blood cells in the standard form.

Solution: The average size of blood cells in a human body is 0.000015 m

0.000015 = 1.5 × 10 -5 m

Thus, we can say that the numbers when written in the standard form are much easier to read, understand and compare than when they are written in their actual form.

Practice Questions

• Write the decimal number, 899.57, in standard form.
• What is the standard form of decimal number 0.00034?
• How to write 454000 in standard form?
• Convert 9.8000 x 10 -3 in decimal number.

Frequently Asked Questions on Standard form of a Number

What is the standard form of a number, what is the standard form of decimal numbers, are the standard form and standard notation of decimal numbers, same, how to convert a decimal number into standard form, write 0.00001487 in standard form..

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Solution - Scientific notation/Standard form

Other Ways to Solve

• Alternative approach

Step-by-step explanation

1. make the number a new number between 1 and 10.

Move the decimal point to make 0.00147 a new number between 1 and 10. Because our original number is less than one, we move the decimal point to the right. Drop any zeroes in front of the number. Keep track of how many times we move the decimal point.

0.00147 -> 1.47

Our new number is 1.47. We moved the decimal point 3 times.

2. Define the power of 10

Because our original number was less than one, the exponent defining the power of 10 is negative. Remember, we moved the decimal point 3 times, so the exponent is negative 3

10 − 3

3. Final result

1.47 ⋅ 10 − 3

How did we do?

Why learn this

Scientific notation, or standard form, makes things easier when working with very small or very big numbers, both of which come up frequently in the fields of science and engineering. It is used in science, for example, to convey the mass of the heavenly bodies: Jupiter’s mass is 1.898 ⋅ 10 27 kg, which is easier to comprehend than writing the number 1,898 followed by 24 zeroes. Scientific notation also makes solving problems that use such high or low numbers more straightforward.

Terms and topics

• Scientific notation

Related links

• How to Write in Scientific Notation | Dummies
• Concept of Scientific Notation | Brightstorm
• Introduction to scientific notation | Khan Academy

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