Year 7 Interactive Maths - Second Edition

## Recurring Decimals

So far, we have considered divisions with a limited number of decimal places in the quotient (i.e. answer).

These are examples of terminating decimals.

Sometimes when dividing, the division will never stop as there is always a remainder.

It is clear that if 8 is divided by 3, then the sixes in the answer never stop.  This is an example of a recurring decimal.

This is written as:

The dot above 6 means that it is repeated indefinitely (i.e. forever).

An alternative notation involves placing a bar above the repeating digit(s) in the quotient (i.e. answer).

#### Example 40

##### Solution:

We notice that the remainder is always 2.  So, the digit in the quotient will continue to be 6.

This is written as:

#### Example 41

Write the decimal 0.3333… in recurring decimal form.

#### Example 42

Write the decimal 4.27777… in recurring decimal form.

#### Example 43

##### Solution:

We notice that the digits 5, 7, 1, 4, 2 and 8 begin to repeat.

This is written by placing a dot over the first and the last recurring digit.

Alternatively, we can write it by placing a bar above the whole repeating set of digits.