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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.
Solution:
Example 42
Write the decimal 4.27777… in recurring decimal form.
Solution:
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.
Example 44
Solution:
Key Terms
terminating decimals, recurring
decimals
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