Lemmara logoLemmaraWorked solution

0580/21 May/Jun 2026, Question 13: Recurring Decimals

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 4 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Work with recurring decimals: subtract 0.924 recurring from 0.213 and give a 5 decimal place answer, then convert 0.67 recurring to a fraction.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 2 marks

Subtract 0.213 from 0.924 recurring, giving the decimal answer correct to 5 decimal places.

  1. 10.92̇4̇ = 0.924242424…
  2. 20.924242424… − 0.213 = 0.711242424…
  3. 3= 0.71124 (5 d.p.)

Answer0.71124

Part (b) · 2 marks

Express the recurring decimal 0.67 recurring as a fraction.

  1. 1Let x = 0.6777…
  2. 2100x = 67.777…, 10x = 6.777…
  3. 390x = 61
  4. 4x = 61/90

Answer61/90

Stuck on a step? Read the free lesson: Recurring Decimals

Practise more recurring decimals questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on recurring decimals

Also searched as: 0580/21/M/J/26 · 0580_s26_qp_21 · 0580 s26 21 · question 13.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.