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

DifficultyAll Level 3 Level 4 Level 5

1
Use algebra to show that $0.\dot{4}\dot{2} + 0.3\dot{5}\dot{7} = \dfrac{m}{55}$ , where $m$ is an integer.

(3 marks)
Level 5 · 3 marksTry it
2
$x = 0.\dot{7}$ and $y = 0.1\dot{6}\dot{3}$

Express $xy$ as a fraction in its simplest form.

(5 marks)
Level 5 · 5 marksTry it
3
Prove algebraically that the recurring decimal $2.1\dot{3}\dot{6}$ can be written as $\dfrac{47}{22}$
Level 5 · 3 marksTry it
4
Prove algebraically that the recurring decimal $1.\dot{2}\dot{0}\dot{7}$ can be written as $\dfrac{134}{111}$
Level 5 · 3 marksTry it