GCSE · Fractions & decimals

Recurring decimals and fractionsExam-style questions

Why the ×10ⁿ-and-subtract trick turns any recurring decimal into a fraction, how to choose the right multiplier, and which fractions terminate (and why the denominator's primes decide it).

Start practising Read the lesson

14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 3Level 4Level 5
  1. 1
    Write the recurring decimal 0.7˙2˙0.\dot{7}\dot{2} as a fraction in its simplest form. (3 marks)
    Level 3 · 3 marksTry it
  2. 2
    Prove algebraically that the recurring decimal 0.8˙0.\dot{8} can be written as 89\dfrac{8}{9}
    Level 3 · 2 marksTry it
  3. 3
    Without working out any division, decide whether each fraction is equal to a terminating decimal or a recurring decimal.

    Give a reason for each answer.

    (a) 940\dfrac{9}{40}

    (b) 712\dfrac{7}{12}
    Level 3 · 2 marksTry it
  4. 4
    (a) Write the recurring decimal 0.4˙0.\dot{4} as a fraction.

    (b) Hence write 5.4˙5.\dot{4} as an improper fraction.
    Level 3 · 3 marksTry it
  5. 5
    Prove algebraically that the recurring decimal 0.2˙7˙0.\dot{2}\dot{7} can be written as 311\dfrac{3}{11} (3 marks)
    Level 4 · 3 marksTry it

9 more questions on recurring decimals and fractions

Free with an account — just an email, no card. The whole bank, every mark scheme and worked solution.

Start free