Converting a Fraction to a Repeating Decimal - Basic

There are certain decimals, where a digit or a group of digits after the decimal point keep repeating and do not end and they go on forever. Such decimals are called repeating decimals.

For example, following are repeating decimals.

$\frac{1}{3} = 0.333333…$

$\frac{1}{6} = 0.166666…$

$\frac{2}{9} = 0.22222…$

$\frac{1}{7} = 0.142857142857…$

The repeating digit or group of digits in a repeating decimal are represented by writing a bar over the repeating digit or group of digits. The following examples show how this is done.

$\frac{4}{3} = 1.3333333… = 1.\bar{3}$

$\frac{1}{7} = 0.142857142857…= 0.\overline{142857}$

$\frac{5}{6} = 0.8333333… = 0.\overline{83}$

$\frac{2}{11} = 0.\overline{18}$

Convert $\frac{2}{3}$ into a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Solution

Step 1:

At first, we set up the fraction as a long division problem, dividing 2 by 3

Step 2:

We find that on long division $\frac{2}{3} = 0.66666...$

Step 3:

The digit 6 keeps on repeating, so we write a bar over 6.

So, $\frac{2}{3} = 0.66666... = 0.\bar{6}$

Convert $\frac{50}{66}$ into a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.

Solution

Step 1:

At first, we set up the fraction as a long division problem, dividing 50 by 66

Step 2:

We find that on long division $\frac{50}{66} = 0.75757575...$

Step 3:

The group of digits 75 keep on repeating, so we write a bar over 75

Step 4:

So, $\frac{50}{66} = 0.757575.. = 0.\overline{75}$