Decimal to Fraction

The basic idea of converting a decimal to a fraction is to rewrite any decimal in fractional form. Turning decimals into fractions is a widespread activity we carry out in our daily lives. Once we learn the steps, we can convert any decimal to a fraction at the drop of a hat.

Steps to Convert Decimals to Fractions

The steps to write decimals in fraction are illustrated pictorially below. Once we learn them, we can mentally change decimals to fractions.

1. Rewrite the fraction with a denominator of 1.
2. Multiply the numerator and denominator by 10n, where, n = no. of digits after the decimal point.
3. Reduce the fraction.

Convert 0.67 to fraction.

Solution:

0.67
= 0.67/1
= ${\dfrac{0.67 × 100}{1 × 100}}$ (The number of digits after the decimal point is 2, so ultiplying with 100)
= Since 67/100 can’t be reduced, therefore, the final fraction is 67/100

Convert the 0.124 to fraction.

Solution:

0.124
= 0.124/1
= ${\dfrac{0.124 × 1000}{1 × 1000}}$ (The number of digits after the decimal point is 3, so multiplying with 1000)
= Reducing: ${\dfrac{124}{1000}}$, the final fraction is ${1\dfrac{31}{250}}$

How to Convert a Negative Decimal to a Fraction

1. Remove the negative sign.
2. Perform the conversion for the positive decimal as in the steps above.
3. Put the negative sign before the simplified fraction. That is the final fraction.

Convert the -0.0625 to fraction.

Solution:

We will ignore the ‘-‘sign and simply work on the value.
So, 0.0625
= ${\dfrac{0.0625}{1}}$
= ${\dfrac{0.0625 × 10000}{1 × 10000}}$
Reducing ${\dfrac{625}{10000}}$
= ${\dfrac{1}{16}}$
= The final fraction is ${\dfrac{-1}{16}}$

We have already learnt how to convert repeating decimals to fraction. Here is an example below to recapitulate it with a larger number.

Converting a REPEATING DECIMAL to a Fraction

Convert 0.5151… to fraction.

Solution:

Let us assume x = 0.5151…. (1)
The repeating period is 2 here, i.e., 5 and 1 is repeating in the same sequence over and over again,
100x = 100 × 0.5151…. (Multiplying 100 with both sides)
100x = 51.5151… (2)
Subtracting (1) from (2)
We get: 100x – x = 51.5151- 0.5151
99x = 51
x = ${\dfrac{51}{99}}$

In order to convert some common decimals to fractions, we can follow the decimal to fraction chart.