MathsYears 10–11Number

Recurring decimals to fractions

Convert recurring decimals to fractions using algebraic proof

What you'll learn

  1. 1

    A recurring decimal like 0.333... means the 3 repeats forever. You can turn it into a fraction!

  2. 2

    Let's turn 0.333... into a fraction together.

  3. 3

    What is the first step to turn 0.666... into a fraction?

  4. 4

    Now try 0.777... – use the number line to see the pattern, then find the fraction.

  5. 5

    What about 0.121212...? The repeating part is 2 digits long.

  6. 6

    What do you multiply by if 3 digits repeat (like 0.123123...)?

  7. 7

    Turn 0.555... into a fraction. What is it?

Practise Recurring decimals to fractions with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 14–16. Aligned to the UK National Curriculum.