1.3.1 Recurring Decimals

1.3.1 Recurring Decimals

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


Course Intro Video

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