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Edexcel IGCSE Maths (4MA1) · Unit 1: Number

IGCSE Maths Recurring Decimals Questions and Answers

Recurring Decimals questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the worked example first, then try the 3 exam-style questions yourself and check your working against the mark scheme.

Practise recurring decimals in Unit 1 →Recurring Decimals revision notes

What this topic covers

Recurring Decimals worked examples

Worked example 1: Recurring decimal to fraction

Write \(0.\dot{5}\dot{4}\) as a fraction in its simplest form.

Solution

  1. Let \(x=0.545454\ldots\), so \(100x=54.5454\ldots\)
  2. Subtract: \(99x=54\).
  3. \(x=\dfrac{54}{99}=\dfrac{6}{11}\).

Answer: \(\tfrac{6}{11}\)

Tip: Multiply by 10ⁿ where n is the length of the repeating block.

Recurring Decimals exam-style questions

Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 1 mark

Write \(0.\dot{4}\) as a fraction.

Show the answer and mark scheme
  • B1 4/9

Answer: \(\tfrac{4}{9}\)

Question 2 · medium · 3 marks

Write \(0.2\dot{3}\) as a fraction in its simplest form.

Show the answer and mark scheme
  • M1 two recurring decimals whose difference is a terminating decimal, e.g. 100x = 23.33… and 10x = 2.33…
  • M1 90x = 21 or 21/90
  • A1 7/30

Answer: \(\tfrac{7}{30}\)

Question 3 · hard · 3 marks

Write \(2.1\dot{3}\dot{6}\) as an improper fraction in its simplest form.

Show the answer and mark scheme
  • M1 e.g. 1000x = 2136.3636… and 10x = 21.3636…
  • M1 990x = 2115
  • A1 47/22

Answer: \(\tfrac{47}{22}\)

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise recurring decimals for the exam

Questions students ask

Which Edexcel IGCSE Maths papers test recurring decimals?

Either Higher tier paper, 1H or 2H, can test recurring decimals: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more recurring decimals questions?

In the IGCSE student hub: Unit 1 (Number) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

More Unit 1 topics: Number