How to convert decimals to fractions

How to Convert Decimals to Fractions

Welcome to the Math Salamanders Convert Decimal to Fraction support page. Here you will find information and support about how to convert a decimal number into a fraction.

We have several worked examples and also a help video to help you understand this concept.

Here you will find some simple information and advice about how to convert a decimal to a fraction.

Before you learn how to do this, you should also know how to simplify fractions.

At the bottom of this page you will also find a printable resource sheet and some practice sheets which will help you understand and practice this math skill.

  • If you want to convert a decimal into a fraction, please use this link to our decimal to fraction calculator.
  • The calculator will convert any decimal to a decimal fraction, and also display the fraction in simplest form.
  • Using the calculator is a great way of self-checking your work to help you with your decimal and fraction learning.

How to Convert Decimals to Fractions

  • Decimal to Fraction Calculator

This short video clip shows how to convert a decimal into a fraction.

To convert a decimal to a fraction, you need to follow the 3 or 4 steps below:

  • Step 1) Count the number of decimal places the decimal has.
  • Step 2) Put a 1 and the number of zeros that there are decimal places for the denominator of the fraction. If you have 2 decimal places, the denominator would be 100. If you have 4 decimal places, the denominator would be 10000.
  • Step 3) The decimal digits now become the numerator.
  • Step 4) Optional – you can reduce this fraction to its simplest form.

How to Convert Decimals to Fractions

Examples

  1. The number of decimal places is 3, so the denominator will be 1000 and the numerator will be 815.
  2. The decimal fraction will be: [ {815 over 1000} ]
  3. To find the simplest form, divide the numerator and denominator by 5.
  4. [ {815 over 1000} = {815 ÷ 5 over 1000 ÷ 5} = {163 over 200} ]
  5. Final answer: [ 0.815 ; = ; {163 over 200 } ]

Example 2) Convert 2.36 to a mixed fraction

The decimal part is 0.36. The number of decimal places is 2. The denominator will be 100. The numerator will be 36.

  • The fraction will be: [ {36 over 100}]
  • To simplify the fraction, divide the numerator and denominator by 4.
  • This gives us: [ {36 over 100} = {36 ÷ 4 over 100 ÷ 4} = {9 over 25} ]
  • Our final answer is: [ 2.36 ; = ; 2 {9 over 25} ]

Example 3) Convert 1.45 to an improper fraction

The decimal part is 0.45. The number of decimal places is 2. The denominator will be 100. The numerator will be 145.

  1. So the improper fraction will be: [ {145 over 100} ]
  2. To simplify the fraction, divide the numerator and denominator by 5.
  3. This gives us: [ {145 over 100} = {145 ÷ 5 over 100 ÷ 5} = {29 over 20} ]
  4. Our final answer is: [ 1.45 ; = ; {29 over 20} ]
  • Here is a printable version of the support sheet.
  • We have a dedicated page on converting decimals to fractions worksheets.
  • These sheets will give you practice converting from decimals or mixed decimals into fractions.

Here you will find some simple information and advice about how to convert a fraction to a decimal.

You will also find a printable resource sheet which explains about how to convert fractions to decimals in a little more detail.

How to Convert Decimals to Fractions

  • Convert Fractions to Decimal

How to Print or Save these sheets

Need help with printing or saving? Follow these 3 easy steps to get your worksheets printed out perfectly!

How to Print or Save these sheets

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Need help with printing or saving? Follow these 3 easy steps to get your worksheets printed out perfectly!

  1. The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

Decimal to Fraction: 3 Easy Steps — Mashup Math

  • Are you ready to learn how to convert a decimal to fraction?
  • (and if you’re looking to learn how to convert a fraction to a decimal, click here)
  • Before you learn an easy way to complete both of these conversions (with and without a calculator), let’s make sure that you understand what decimals and fractions are:
  •  A decimal number is used to represent a non-whole number where a decimal point is used followed by digits that represent a value that is smaller than one.
  • A fraction represents a part of a whole number. A fraction is a ratio between the upper number (the numerator) and the lower number (the denominator). The numbers are stacked vertically and separated with a bar.

The key takeaway from these definitions is that decimals and fractions are different ways of representing the same thinga number that is not whole.

You can convert a decimal to a fraction by following these three easy steps.

In this case, you will use the decimal 0.25 as an example (see the graphic below).

Step One: Rewrite the decimal number over one (as a fraction where the decimal number is numerator and the denominator is one).

Step Two: Multiply both the numerator and the denominator by 10 to the power of the number of digits after the decimal point. If there is one value after the decimal, multiply by 10, if there are two then multiply by 100, if there are three then multiply by 1,000, etc.

In the case of converting 0.25 to a fraction, there are two digits after the decimal point. Since 10 to the 2nd power is 100, we have to multiply both the numerator and denominator by 100 in step two.

Step Three: Express the fraction in simplest (or reduced form).

If you need more help with simplifying fractions, check out this free video lesson.

By following these three steps in the above decimal to fraction example, you can conclude that the decimal 0.25, when converted to a fraction, is equal to 1/4.

Here is another example of how to convert a decimal to fraction:

How to Convert Decimals to Fractions

Notice that the answer to this example is a mixed number (a whole number and a fraction combined).

How to Convert Decimals to Fractions

If you need a fast and easy way to convert a decimal to a fraction, then you can take advantage of the many free online decimal to fraction conversion calculators that are available.

This free decimal to fraction calculator from www.calculatorsoup.com not only performs the conversion, but also shows the calculations (using the three step method shown above), which is a handy tool since it will not only help you find a correct answer, but also understand the process as well.

To use the decimal to fraction calculator, simply input the decimal value and press calculate. Depending on the value that you input, the calculator will convert the decimal to a fraction or a mixed number.

How to Convert a Decimal to a Fraction

How to Convert Decimals to Fractions

Knowing how to convert a decimal to a fraction is a handy skill. It’s not only useful on math tests, but also in real-life situations where you want to do a part to whole comparison. Multiplying fractions is also arguably simpler than multiplying decimals. In this post, we’ll break this skill down into steps so that you can quickly do these conversions whenever you encounter them, whether it’s real life or on a test.

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Though the concept might seem difficult at first, converting a decimal to a fraction can be done in just a few simple steps.

First, you need to confirm that the decimal you’re working with is a terminating one. This means it has a finite number of digits rather than a sequence of repeating digits that continue infinitely. Some examples of terminating decimals are: (.25,:.782,:.9672154,) etc. Most decimals are terminating, and this is a good news since these are the easiest decimals to convert to a fraction.

Once you know that a decimal is terminating, follow the steps below to convert it to a fraction.

How to Convert a Terminating Decimal to a Fraction

Step 1: Create a fraction by putting the decimal over 1.

Write the decimal as a fraction, with the decimal as the numerator and (1) as the denominator. So, for example, if you’re given the decimal (.38), you will write it as:

(frac{.38}{1})

Step 2: Multiply by the right power of 10 to get rid of the fraction.

Next you’ll need to get rid of the decimal in the fraction you just created. You can’t simply erase it, though, You’ll first need to account for place value. If you know your place value, you know that the decimal (.38) is read 38 hundredths, which gives you an important clue about what the denominator is about to become.

If you don’t know your place values, though, no need to worry; there’s a simple trick to help you out. Simply count the number of digits to the right of the decimal. In the example above there are two. So, you’ll need to multiply both sides of the fraction by (10), two times:

(frac{.38: imes:10: imes:10}{1: imes:10: imes:10}=frac{38}{100})       

As you can see in the example above, the decimal (.38) then converts to the fraction (frac{38}{100}), but your job isn’t done yet.

Step 3: Reduce the fraction using common factors.

Your last step is reducing the fraction. To do this you need to find common factors of both the numerator and the denominator, and divide each by them again and again until you cannot reduce the numbers any further.

In the example above, both (38) and (100) can be divided by (2), and then divided by (2) again. See how it works below:

(frac{38:div:2}{100:div:2}=frac{19}{50})

Because (19) and (50) do not have any more common factors, this fraction cannot be reduced any further. Therefore we now know that:

(.38=frac{19}{50})

Let’s look at a simple example. To convert the common decimal (.2) to a fraction you’d follow the same steps.

Example 1:

Step 1:

(frac{.2}{1})

Step 2:

(frac{.2: imes:10}{1: imes:10}=frac{2}{10})

Step 3:

(frac{2:div:2}{10:div:2}=frac{1}{5})

So, we now know that:

(.2=frac{1}{5})

Let’s take a look at another, more complicated example. Let’s convert (.8535) to a fraction.

Example 2:

Step 1:

(frac{.8535}{1})

Step 2:

(frac{.8535: imes:10: imes:10: imes:10: imes:10}{1: imes:10: imes:10: imes:10: imes:10}=frac{8535}{10000})

Step 3:

(frac{8535:div:5}{10000:div:5}=frac{1707}{2000})

Because (1707) and (2000) have no more factors in common, the fraction cannot be reduced further. Therefore:

(.8535=frac{1707}{2000})

The 3 Steps to Convert Decimals to Fractions (and Back)

How to Convert Decimals to Fractions

Wondering how to convert decimals to fractions? Or how to convert fractions to decimals? It’s easier than you think! Keep reading to see the steps for decimal to fraction conversions (including why you need to follow different steps if you have a repeating decimal), steps for fraction to decimal conversions, a handy chart with common decimal/fraction conversions, and tips for quickly estimating conversions.

See also:  How to simplify fractions

How to Convert Decimals to Fractions

How do you convert a decimal to a fraction? Any decimal, even complicated-looking ones, can be converted to a fraction; you just need to follow a few steps. Below we explain how to convert both terminating decimals and repeating decimals to fractions.

Converting a Terminating Decimal to a Fraction

A terminating decimal is any decimal that has a finite other of digits. In other words, it has an end. Examples include .5, .234, .864721, etc. Terminating decimals are the most common decimals you’ll see and, fortunately, they are also the easiest to convert to fractions.

Step 1

Write the decimal divided by one.

Decimal to fraction conversion

Decimals are fractions that have powers of ten as their denominators. Or, to say another way, they have 10, 100, 1000, and so on as the bottom number of the fraction.

The main thing when we convert from decimal to common fractions is to find out what we are dealing with. Is it tenths? Is it hundredths? Or is it thousandths?

The examples below show decimals can be shown as common fractions.

We write as a decimal We read, or say We write as a common fraction
.3 . 3 three tenths
.7 . 7 seven tenths
.23 . 2 3 twenty-three hundredths
.61 . 6 1 sixty-one hundredths
.597 . 5 9 7 five hundred ninety-seven thousandths
.439 . 4 3 9 four hundred thirty-nine thousandths

The place value of the number on the right tells whether the common fraction is in tenths, hundredths, thousandths, and so on.

Decimal to Fraction Calculator

Fraction to decimal converter ►

  1. Write the decimal fraction as a fraction of the digits to the right of the decimal period (numerator) and a power of 10 (denominator).
  2. Find the greatest common divisor (gcd) of the numerator and the denominator.
  3. Reduce the fraction by dividing the numerator and the denominator with the gcd.
  • Convert 0.32 to fraction:
  • 0.32 = 32/100
  • Find the greatest common divisor (gcd) of the numerator and the denominator:
  • gcd(32,100) = 4
  • Reduce the fraction by dividing the numerator and the denominator with the gcd:
  • 0.32 = (32/4) / (100/4) = 8/25

Example #2

  1. Convert 2.56 to fraction:
  2. 2.56 = 2+56/100
  3. Find the greatest common divisor (gcd) of the numerator and the denominator:
  4. gcd(56,100) = 4
  5. Reduce the fraction by dividing the numerator and the denominator with the gcd:
  6. 2+56/100 = 2 + (56/4) / (100/4) = 2+14/25

Example #3

  • Convert 0.124 to fraction:
  • 0.124 = 124/1000
  • Find the greatest common divisor (gcd) of the numerator and the denominator:
  • gcd(124,1000) = 4
  • Reduce the fraction by dividing the numerator and the denominator with the gcd:
  • 0.124 = (124/4) / (1000/4) = 31/250

How to convert repeating decimal to fraction

Example #1

Convert 0.333333… to fraction:

x = 0.333333…

10x = 3.333333…

10x – x = 9x = 3

x = 3/9 = 1/3

Example #2

Convert 0.0565656… to fraction:

x = 0.0565656…

100x = 5.6565656…

  1. 100x – x = 99x = 5.6
  2. 990x = 56
  3. x = 56/990 = 28/495

Decimal to fraction conversion table

Decimal Fraction
0.00001 1/100000
0.0001 1/10000
0.001 1/1000
0.01 1/100
0.08333333 1/12
0.09090909 1/11
0.1 1/10
0.11111111 1/9
0.125 1/8
0.14285714 1/7
0.16666667 1/6
0.2 1/5
0.22222222 2/9
0.25 1/4
0.28571429 2/7
0.3 3/10
0.33333333 1/3
0.375 3/8
0.4 2/5
0.42857143 3/7
0.44444444 4/9
0.5 1/2
0.55555555 5/9
0.57142858 4/7
0.6 3/5
0.625 5/8
0.66666667 2/3
0.7 7/10
0.71428571 5/7
0.75 3/4
0.77777778 7/9
0.8 4/5
0.83333333 5/6
0.85714286 6/7
0.875 7/8
0.88888889 8/9
0.9 9/10
1.1 11/10
1.2 6/5
1.25 5/4
1.3 13/10
1.4 7/5
1.5 3/2
1.6 8/5
1.7 17/10
1.75 7/4
1.8 9/5
1.9 19/10
2.5 5/2

Fraction to decimal conversion ►

See also

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