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

Edexcel IGCSE 4MA1 Recurring Decimals: Exam 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 8 exam-style questions yourself and check your working against the mark scheme.

1 worked example
8 questions with mark schemes
Higher tier · calculator allowed
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Practise recurring decimals in Unit 1 →Recurring Decimals revision notes

What this topic covers

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 $x = 0.545454 \dots$ , so $100 x = 54.5454 \dots$
Subtract: $99 x = 54$ .
$x = \frac{54}{99} = \frac{6}{11}$ .

4 steps · 1 to fill in

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 (one has its full worked solution open). 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: $\frac{4}{9}$

Question 2 · easy · 2 marks

Write the recurring decimal $0. \dot{3} \dot{6}$ as a fraction in its simplest form.

Show the answer and mark scheme

M1 e.g. 100x − x = 36.3636… − 0.3636… = 36, or 36/99
A1 4/11

Answer: $\frac{4}{11}$

Question 3 · easy · 2 marks

Prove algebraically that the recurring decimal $0. \dot{1} \dot{8} = \frac{2}{11}$ .

Show the answer and mark scheme

M1 x = 0.1818… and 100x = 18.1818… with intention to subtract
A1 99x = 18 ⇒ x = 18/99 = 2/11 (cso)

Answer: $\frac{2}{11}$ (shown)

Question 4 · medium · 3 marks

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

Full worked solution Free, no sign-in

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: $\frac{7}{30}$

Every question here has a full worked solution. See them all →

Question 5 · medium · 2 marks

Use algebra to show that the recurring decimal $0. \dot{9}$ is exactly equal to 1.

Show the answer and mark scheme

M1 x = 0.999… and 10x = 9.999… with intention to subtract
A1 9x = 9 ⇒ x = 1 (cso)

Answer: 1 (shown)

Question 6 · 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: $\frac{47}{22}$

Question 7 · hard · 2 marks

Write $0. \dot{0} 4 \dot{5}$ (that is, 0.045045045…) as a fraction in its simplest form.

Show the answer and mark scheme

M1 1000x − x = 45 or 45/999
A1 5/111

Answer: $\frac{5}{111}$

Question 8 · very hard · 3 marks

Work out $0. \dot{2} + 0. \dot{0} \dot{3}$ . Give your answer as a fraction in its simplest form.

Show the answer and mark scheme

M1 0.2̇ = 2/9 oe
M1 0.0̇3̇ = 3/99 oe (= 1/33)
A1 25/99

Answer: $\frac{25}{99}$

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

Unit 1 practice: Number in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

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.

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Edexcel IGCSE 4MA1 Recurring Decimals: Exam Questions and Answers

Try it first

What this topic covers

Recurring Decimals worked examples

Worked example 1: Recurring decimal to fraction

Solution

Recurring Decimals exam-style questions

Question 1 · easy · 1 mark

Question 2 · easy · 2 marks

Question 3 · easy · 2 marks

Question 4 · medium · 3 marks

Full worked solution Free, no sign-in

Question 5 · medium · 2 marks

Question 6 · hard · 3 marks

Question 7 · hard · 2 marks

Question 8 · very hard · 3 marks

Revise recurring decimals for the exam

Questions students ask

Practise recurring decimals with your progress saved

More Unit 1 topics: Number