What are recurring decimals?
A rational number is any number that can be written as an integer (whole number) divided by another integer. When you write a rational number as a decimal you either get a decimal that stops (eg ¼ = 0.25) or one that recurs (eg ⅓ = 0.333333…).
The recurring part can be written with a dot (or dots) over it instead as in the example below.
What do we do with recurring decimals?
Normally, you will be asked to write a recurring decimal as a fraction in its lowest terms.
To do this:
Write out a few decimal places… …and then:
- Write as f = …
- Multiply by 10 repeatedly until two lines have the same decimal part
- Subtract those two lines
- DIVIDE to get f = … (and cancel if necessary to get fraction in lowest terms)