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
A fraction whose denominator has only factors of 2 and 5 gives a terminating decimal. Any other factor gives a recurring one.
- 2
A dot over a digit shows it repeats. 0.3̇ means 0.3333... and 0.1̇2̇ means 0.121212...
- 3
Which fraction gives a recurring decimal?
- 4
0.3̇ is exactly one third, not approximately. Writing 0.33 loses accuracy and can cost marks.
- 5
Convert 0.4̇ to a fraction. Let x = 0.444... Then 10x = 4.444... Subtract: 9x = 4, so x = 4/9.
- 6
What is 0.6̇ as a fraction?
- 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.