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).

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

DifficultyAllLevel 3Level 4Level 5
  1. 1
    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
  2. 2
    Write the recurring decimal 0.5˙4˙0.\dot{5}\dot{4} as a fraction in its simplest form.
    Level 4 · 2 marksTry it
  3. 3
    Write 0.38˙0.3\dot{8} as a fraction in its simplest form.
    Level 4 · 3 marksTry it
  4. 4
    Write the recurring decimal 0.2˙7˙0.\dot{2}\dot{7} as a fraction in its simplest form.
    Level 4 · 3 marksTry it
  5. 5
    Prove algebraically that 0.16˙=160.1\dot{6} = \dfrac{1}{6}
    Level 4 · 3 marksTry it

1 more question on recurring decimals and fractions

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