Decimal fractions are those in which the denominators are powers of 10.

$\frac{1}{10}$ , $\frac{1}{100}$, $\frac{1}{1000}$ are respectively the tenth, the hundredth and the thousandth part of 1. $\frac{8}{10}$ is 8 tenths written in decimals as 0.8, $\frac{14}{100}$ is 14 hundredths written in decimals as 0.14, $\frac{6}{1000}$ is 6 thousandths written in decimals as 0.006 and so on.

## Expressing Common Fraction as Decimal Fraction

Let us first understand what a common fraction is. A fraction as a term would mean a type of division which is considered as a part or piece of a whole or that which indicates the division of a whole into equal units or parts. A common fraction would therefore definitely refer to an expression where the denominator would be the same for all fractions like $\frac{1}{5}$, $\frac{2}{5}$, etc.

The expression if and when expressed in decimals would qualify as a decimal fraction so for each of the common fractions like $\frac{1}{5}$, $\frac{2}{5}$ or $\frac{3}{5}$ can be expressed in decimal terms as well.

$\frac{1}{5}$ = 0.2

$\frac{2}{5}$ = 0.4

$\frac{3}{5}$ = 0.6

Common fraction is in fact another way of indicating division and is nothing but getting the numerator divided by the denominator into decimals. To change a common fraction into its decimal fraction we need to follow the steps mentioned below.

Step 1: The numerator is divided by the denominator.
Step 2: Carry the division beyond the needed number of decimal places by one digit.
Step 3: Round off the quotient wherever required to the number of decimal places.

### Examples on Expressing a Common Fraction as a Decimal Fraction

Here are some examples based on common fraction as a decimal fraction:

Example 1:

Find the decimal fractions of common fractions $\frac{2}{12}$ , $\frac{5}{6}$ and $\frac{7}{6}$

Solution : Given $\frac{2}{12}$ , $\frac{5}{6}$ and $\frac{7}{6}$

Step 1: Convert the fractions into its lowest equivalents ($\frac{2}{12}$ = $\frac{2\times1}{2\times6}$ = $\frac{1}{6}$ )

Step 2: Convert into common fractions ( $\frac{1}{6}$ , $\frac{5}{6}$ and $\frac{7}{6}$ )

Step 3: Convert into decimals (0.1667) , (0.8333) and (1.1667)

Example 2:

Find the decimal fractions of common fractions $\frac{2}{7}$, $\frac{6}{14}$, and $\frac{4}{7}$

Solution:

Basic idea: Convert the fractions into common fractions

Step 1: Convert the fractions into its lowest equivalents ( $\frac{6}{14}$ = ($\frac{2\times3}{2\times7}$) = $\frac{3}{7}$ )

Step 2: Convert into common fractions ( $\frac{2}{7}$, $\frac{3}{7}$, $\frac{4}{7}$ )

Step 3: Convert into decimals (0.2857) (0.42857) (0.57142857)

### Numerator Denominator

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