0580/21 May/Jun 2024, Question 15: Recurring Decimals
Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 3 marks
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The question, in short
Convert the recurring decimal 0.146146... (digits 14 then 6 repeating) into a fraction in lowest terms, showing every step of the method.
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Solution · 3 marks
- 1Let x = 0.1464646…
- 21000x = 146.4646… and 10x = 1.4646…
- 3990x = 146.4646… − 1.4646… = 145
- 4x = 145/990 = 29/198
Answer29/198
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