 # Convert Decimal to Fraction

In order to convert decimal to fraction, we need to know about the numbers we use in arithmetic operations. We can easily convert a decimal number into a fraction by following simple steps and no calculators are required. We will elaborate here all the steps with examples. Let us learn about decimal and fraction first.

Decimal: In terms of computer, decimal numbers are the numbers which have base 10. But in Mathematics, a decimal number is a number which has a dot(.) or decimal point between somewhere. Basically, decimals are nothing but the fractions with denominator as 10 or multiples of 10.

Fractions: Fraction is a part of a whole number. It is denoted as a ratio of two numbers a/b, where a and b are integers, also b≠0. The two numbers are called the numerator and denominator. We can perform all the arithmetic operations on fractions. There are three types of fractions, Proper, Improper and Mixed.

## How to Convert Decimal Number into Fractions?

Now let us learn the steps to convert the decimal into fractions.

1. Firstly, count the numbers after the decimal point or right side of the decimal point.
2. If n is the number of digits on the right side of the decimal point, then multiply and divide the whole number by 10n to remove the decimal from the numerator.
3. After that, you can simplify the number, by reducing the numerator and denominator.
4. The resultant will be the required fraction from the given decimal number.

## Decimal to Fraction Examples

Question 1: Find the fraction form of the decimal 0.7

Solution: Given, decimal number 0.7, we need to find the fraction for 0.7.

We can also find a number of equivalent fractions by finding its multiples.

0.7 = 7/10

Now multiply, 7/10 by 2, both in numerator and denominator, then we get;

(7×2)/(10×2) = 14/20

To find more equivalent fractions, let us multiply 7/10 by 5 and 10 both in numerator and denominator.

7×5/10×5 = 35/50

7×10/10×10 = 70/100

Therefore, the fractions of 0.7 decimal are 7/10, 35/50, 70/100.

Question 2: Convert 7.15 into a fraction.

Solution: Given, 7.15 is a decimal number.

Multiply and divide 7.15 by 100.

7.15 × 100/100 = 715/100

If we simplify it more, we get;

143/20

We can also find the equivalent fractions by multiplying the numerator and denominator by 2. Such as;

143×2/20×2 = 286/40

So, 7.15 equivalent fractions are 715/100, 143/20 and 286/40.

## Repeating Decimal to Fraction

To convert a usual decimal number to a fraction is an easy method. But to convert a repeating or recurring number to a fraction is a lengthy task. For example, 0.666…, 4.17777…, 0.56111.., are recurring numbers. Let us learn to convert recurring decimal to fraction with the help of an example.

Example: Convert 0.6666… Into fraction.

Solution: Let x = 0.6666

Now multiply x by 10 on both sides.

10 x = 6.666…

Subtracting x from 10x, we get;

10x-x = 6.666…-0.6666

9x = 6.000

x = 6/9 = ⅔

Hence, 0.6666… = ⅔

### Decimal to Fraction Chart

 Decimal Fraction Decimal Fraction 0.5 1/2 1.5 6/4 0.25 1/4 0.857142… 6/7 0.6666… 2/3 0.875 7/8 0.4 2/5 1.4 7/5 0.285714… 2/7 3.333… 10/3 0.2222 2/9 1.42857… 10/7 0.75 3/4 1.875 15/8 0.428571… 3/7 0.9375 15/16 2.5 5/2 0.95454… 21/22 0.83333 5/6 0.78125 25/32