1.3.1 Recurring Decimals

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:

1. Write as f = …
2. Multiply by 10 repeatedly until two lines have the same decimal part
3. Subtract those two lines
4. DIVIDE to get f = … (and cancel if necessary to get fraction in lowest terms)

Worked Example