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4MA1/1HR Jan 2020, Question 13: Recurring Decimals

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 4 marks

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The question, in short

Show a recurring decimal equals 63/110 using algebra, then rationalise a fraction with a surd denominator containing prime y.

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

Part (a) · 2 marks

Use algebra to prove the recurring decimal 0.57272… equals 63/110.

  1. 1Let x = 0.57272...
  2. 2Then 100x = 57.27272...
  3. 3Subtract: 100x − x = 57.27272... − 0.57272...
  4. 499x = 56.7
  5. 5Multiply numerator and denominator by 10: 567 / 990
  6. 6Simplify 567 ÷ 9 = 63, 990 ÷ 9 = 110
  7. 763/110

Answer63/110

Part (b) · 2 marks

Rationalise 3/(2 − √y), giving the result as (a + b√y)/(c − y) with integer a, b, c.

  1. 13/(2 − √y)
  2. 2Multiply numerator and denominator by (2 + √y).
  3. 3Numerator: 3(2 + √y) = 6 + 3√y
  4. 4Denominator: (2 − √y)(2 + √y) = 4 − y
  5. 53/(2 − √y) = (6 + 3√y)/(4 − y)

Answer(6 + 3√y)/(4 − y)

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