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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 fractions have a limited number of decimal places.

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:

This is a recurring decimal.

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.

Solution:


Example 42

Write the decimal 4.27777 in recurring decimal form.

Solution:


Example 43

Write 4  7 in recurring decimal form.

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.


Example 44

Solution:

   


Key Terms

terminating decimals, recurring decimals


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