Recurring Decimals

Recurring Decimals

GCSE(F),

A recurring decimal is a fraction which gives a number that can divided forever. For example, `frac(2)(3)` gives a result of 0.66666... which can continue forever.

To show that it is a recurring decimal, the first 6 is shown with a dot above it, and this 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`.

Examples

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

Answer: Yes, as it evaluates to `0.08dot3`

1 divided by 12 is 0.0833333... Show as a recurring decimal.

2. Evaluate `1.dot(3) xx 3` .

Answer: 4

`1.dot(3) xx 3 `

`= 1frac(1)(3) xx 3`

`= frac(4)(3) xx 3`

`= 4`