Edexcel International GCSE Maths Recurring Decimals Past Paper Questions and Solutions (4MA1 Higher)

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Edexcel International GCSE Maths A (4MA1) · Higher · Numbers and the Number System

Decimals and Recurring Decimals: Edexcel 4MA1 Past Paper Questions and Worked Solutions

This page collects every decimals and recurring decimals question from the Pearson Edexcel International GCSE Mathematics A (4MA1) Higher tier Paper 1H and Paper 1HR, January 2020 to June 2025: 5 questions worth 11 marks. Questions run from easier to harder. Try each one first, then click “Show solution” for a step-by-step method with the reason for every step. All answers are checked against the official Pearson mark schemes.

12 marksHigherJanuary 2023 · Paper 1HR (4MA1/1HR) · Q13

Use algebra to show that 0.38̇1̇ = 21⁄55

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  1. Let x = 0.3818181…
  2. 1000x = 381.818181… and 10x = 3.818181… (both have the same digits after the decimal point)
  3. Subtract: 990x = 378, so x = 378⁄990
  4. Divide top and bottom by 18: 378⁄990 = 21⁄55

Answer: 0.38̇1̇ = 21⁄55 (shown)

22 marksHigherJune 2021 · Paper 1H (4MA1/1H) · Q16

Use algebra to show that the recurring decimal 0.281̇3̇ = 557⁄1980 (the digits 1 and 3 recur, so the decimal is 0.2813131…).

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  1. Let x = 0.2813131…
  2. The recurring block “13” has 2 digits. 1000x = 281.313131… and 10x = 2.813131…
  3. Subtract: 990x = 278.5, so x = 278.5⁄990 = 557⁄1980 (multiplying top and bottom by 2)

Answer: 990x = 278.5, so x = 557⁄1980

32 marksHigherJune 2023 · Paper 1HR (4MA1/1HR) · Q16

Use algebra to show that 0.17̇6̇ = 35⁄198 (the digits 7 and 6 recur, so the decimal is 0.1767676…).

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  1. Let x = 0.1767676…
  2. The recurring block “76” has 2 digits. Find two multiples of x with the same digits after the point: 1000x = 176.767676… and 10x = 1.767676…
  3. Subtract: 990x = 175, so x = 175⁄990
  4. Divide top and bottom by 5: 175⁄990 = 35⁄198

Answer: 990x = 175, so x = 175⁄990 = 35⁄198

42 marksHigherJune 2025 · Paper 1HR (4MA1/1HR) · Q16

Use algebra to show that the recurring decimal 0.61̇2̇ = 101⁄165 (the digits 1 and 2 recur, so the decimal is 0.6121212…).

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  1. Let x = 0.6121212…
  2. The recurring block “12” has 2 digits, so compare 1000x and 10x, which have the same digits after the decimal point.
  3. 1000x = 612.121212… and 10x = 6.121212…
  4. Subtract: 990x = 606, so x = 606⁄990
  5. Simplify by dividing top and bottom by 6: 606⁄990 = 101⁄165

Answer: 990x = 606, so x = 606⁄990 = 101⁄165

53 marksHigherNovember 2021 · Paper 1H (4MA1/1H) · Q18

0.4ẋ is a recurring decimal (the digit x recurs, so it is 0.4xxx…). x is a whole number such that 1 ≤ x ≤ 9. Find, in terms of x, the recurring decimal 0.4ẋ as a fraction. Give your fraction in its simplest form. Show clear algebraic working.

Show solution
  1. Let y = 0.4xxx… Only one digit recurs, so compare 100y and 10y, which have the same digits after the point.
  2. 100y = 4x.xxx… (the number “4x” means 40 + x) and 10y = 4.xxx…
  3. Subtract: 90y = (40 + x) − 4 = 36 + x

Answer: 36 + x⁄90

Tip: Check with x = 9: 0.4999… = 45⁄90 = 0.5 ✓

More Numbers and the Number System questions

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