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Convert Decimal to Fraction

In order to deal with problems related to arithmetic, one needs to have a proper knowledge of numbers and its types. let us see how to convert decimal to fractions. First we will recall what decimals and fractions are.

Decimals :
In computers, a decimal number is a type of number that has base 10. In mathematics, a decimal number is a number that has a point or dot (.) somewhere in the number. The decimal can also define as a fraction with the denominator of 10 or multiples of 10.

A certain part of the whole is called as a fraction.It has one number into another separated by a bar. The two numbers are known as numerator and denominator. The fractions can be denoted as $\frac{a}{b}$ , where a, b are integers; also b $\neq$ 0. All integer operations can be done on fractions. There are three types of fractions in maths - proper fractions, improper fractions and mixed fraction.

A decimal number can be easily converted into a fraction. In order to do so, one needs to count how many digits are there on the right side of the decimal. Then, remove decimal point and put the same number of zeros after 1 in the denominator. It becomes a fraction now. Simplify and find the simplest form of the fraction equivalent to given decimal number.

Related Calculators
Convert a Decimal to a Fraction Calculator Convert a Fraction to a Decimal Calculator

How do you Change a Decimal to a Fraction

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The method of how to convert a decimal to a fraction are given below:

Step 1: Count the number of digits to the right of the decimal point.

Step 2: Let us suppose the number of digits to the right of decimal be p. Then divide the number by $10^{p}$.  Example, if we have 3 digits right of decimal point. Multiply and divide the given number with 1000

Step 3:
Do the simplification if needed.

The result is the equivalent fraction for the given decimal numbers

How to Convert Decimals to Fractions

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Below are examples based on converting decimals into fractions which help you to understand how to convert decimals to fractions :

Solved Examples

Question 1: Find fraction form of the decimal 0.6
Step 1: Given, decimal 0.6, we need to find the fraction for 0.6

Step 2:
We can also find so many equivalent fractions.

0.6 = $\frac{6}{10}$ .

Multiply $\frac{6}{10}$ by 2 , $\frac{6\times2}{10\times2}$

= $\frac{12}{20}$

0.6 = $\frac{6}{10}$ = $\frac{12}{20}$

We can find more equivalent fraction. Multiply $\frac{12}{20}$ by 5 on both numerator and denominator.

$\frac{12\times5}{20\times5}$ = $\frac{60}{100}$

0.6 = $\frac{6}{10}$ = $\frac{12}{20}$ = $\frac{60}{100}$

Step 3:
Multiply and divide 0.6 by 10,

0.6 × $\frac{10}{10}$ = $\frac{0.6*10}{10}$

= $\frac{6}{10}$

0.6 as the fraction $\frac{6}{10}$.

Correct answer is Equivalent fraction of 0.6 are $\frac{6}{10}$ , $\frac{12}{20}$ , $\frac{60}{100}$
Question 2: Convert the the decimal 8.12 into fraction.
Step 1:
We have to find the equivalent fraction of 8.12
Multiply and divide 8.12 by 100 ,
8.12 = 8.12 $\frac{100}{100}$
= $\frac{812}{100}$

Step 2:
Multiply $\frac{812}{100}$ by 2 on both numerator and denominator,

$\frac{812}{100}$ = $\frac{812\times2}{100\times2}$

= $\frac{1624}{200}$

Step 3:
Multiply $\frac{1624}{200}$ by 2 on both numerator and denominator,

$\frac{1624}{200}$ = $\frac{1624\times2}{200\times2}$

= $\frac{3248}{400}$

Correct answer is Equivalent fraction of 8.12 are $\frac{812}{100}$ , $\frac{1624}{200}$ , $\frac{3248}{400}$ .
Question 3: Find the equivalent fraction for the decimal number 0.34
Step 1:

Find out number of digits right to decimal point.

The number of digits after decimal point is 2 .

Step 2:

Now multiply and divide the 0.34 with 100

= 0.34 × $\frac{100}{100}$.

0.34* 100 multiplying it we get the result as 34

= $\frac{34}{100}$.

Step 3:

It can be simplified further.

Now divide numerator and denominator by 2 . We get the simplified answer as


Correct answer is $\frac{17}{50}$

Practice Problems

Question 1: Convert the repeating decimal 0.33333 into fraction
Question 2: Convert the repeating decimal into fraction0.1666667 into fraction
Question 3: Find the equivalent fraction for the decimal number 0.25
Question 4: Find the equivalent fraction for the decimal number 0.50

Decimal to Fraction Chart

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Below you could see the decimal to fraction chart
Decimal to Fraction Chart

Repeating Decimal to Fraction

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Repeating decimals have a digit or a block of digits getting repeated endlessly.
0.333....., 0.416666........, 0.57145714............ are repeating decimals.
If the digits after the decimals are repeated , it is called pure recurring decimals.
Mixed recurring decimals have mixed numbers repeating such as 0.242424....

Decimals can be converted into fractions.
0.25 = $\frac{1}{4}$ and 0.5 = $\frac{1}{2}$
But when the decimal has repeating digits, it becomes necessary to convert them into fractions by using variable x.

Solved Examples

Question 1: Convert 0.7777....... into fraction
Let x = 0.7777

Step1 multiply x by 10

Then 10x = 7.777

Step 2 subtract x from 10 x

Then 10x - x = 7.777 - 0.777

               9x = 7.000

Step 3 Dividing both sides by 9  we get  x = $\frac{7}{9}$

Answer  0.7777...... = $\frac{7}{9}$

Question 2: Convert 0.2424... to fractions.
Let x = 0.2424

Step 1: Multiply  x by 100

Then 100x = 24.2424

Step 2: Subtract x from 100x

100x - x = 24.2424 - 0.2424

        99x = 24

Step 3: Divide both sides by 99

x = $\frac{24}{99}$ which on simplification gives $\frac{8}{33}$

Hence 0.2424.... = $\frac{8}{33}$

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