0580/23 Oct/Nov 2025, Question 20: Recurring Decimals
Cambridge IGCSE Mathematics 0580 · Paper 23 (Extended) · Non-calculator · 3 marks
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The question, in short
Add the recurring decimal 0.114114... to 0.2 and express the result as a fraction.
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Solution · 3 marks
- 10.11̇4̇ + 0.2 = 0.31414…
- 2Let x = 0.31414…: 1000x = 314.1414… and 10x = 3.1414…
- 3990x = 314.14… − 3.14… = 311
- 4x = 311/990
Answer311/990
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