Recurring Decimals

## Recurring Decimals

A recurring decimal is a fraction which gives a decimal number that gfoes on forever. For example, frac(2)(3) gives a result of 0.66666... (and continues forever).

Rather than write 0.666666... forever, and to show that it is a recurring decimal, the first 6 is shown with a dot above it. This dot indicates that this digit repeats forever: 0.dot6.

If a number recurs in pairs, then a dot is placed above the repeating digits:

23.676767676767... can be written as 23.dot6dot7

which indicates that the 67 repeats forever.

If the number repeats over three or more digits, then the dots are shown above the first and last digits of the repeating group:

2.653894894894894... becomes 2.65 dot389dot4.

## Example 1

Does frac(1)(12) evaluate to a recurring decimal?

1 divided by 12 is 0.0833333...

Show as a recurring decimal.

Answer: Yes, as it evaluates to 0.08dot3

## Example 2

Evaluate 1.dot(3) xx 3 .

1.dot(3) xx 3

= 1frac(1)(3) xx 3

= frac(4)(3) xx 3

= 4