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.
Recurring Decimals to Fractions: Converting recurring decimals to fractions using an algebraic method.
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
Let \(x=0.545454\ldots\), so \(100x=54.5454\ldots\)
Subtract: \(99x=54\).
\(x=\dfrac{54}{99}=\dfrac{6}{11}\).
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.
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.