MathsYears 9–11Number

Recurring decimals and exact values

Learn Recurring decimals and exact values for Years 9–11 pupils (ages 13–16). Free practice questions, lessons and worked examples — aligned to the UK National Curriculum.

What you'll learn

  1. 1

    A fraction whose denominator has only factors of 2 and 5 gives a terminating decimal. Any other factor gives a recurring one.

  2. 2

    A dot over a digit shows it repeats. 0.3̇ means 0.3333... and 0.1̇2̇ means 0.121212...

  3. 3

    Which fraction gives a recurring decimal?

  4. 4

    0.3̇ is exactly one third, not approximately. Writing 0.33 loses accuracy and can cost marks.

  5. 5

    Convert 0.4̇ to a fraction. Let x = 0.444... Then 10x = 4.444... Subtract: 9x = 4, so x = 4/9.

  6. 6

    What is 0.6̇ as a fraction?

  7. 7

    Why leave an answer as a fraction rather than a rounded decimal?

Practise Recurring decimals and exact values with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 13–16. Aligned to the UK National Curriculum.