NumberDeep Dive

Converting Recurring Decimal → Fraction

Part of Recurring Decimals · GCSE GCSE Mathematics revision

This deep dive covers Converting Recurring Decimal → Fraction within Recurring Decimals for GCSE Mathematics. Revise Recurring Decimals in Number for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 3 of 6 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 6

Practice

14 questions

Recall

11 flashcards

Converting Recurring Decimal → Fraction

1 Let x = the recurring decimal

2 Multiply by 10, 100, 1000... to shift the decimal point so repeating part lines up

3 Subtract to eliminate the recurring part

4 Solve for x and simplify

Keep building this topic

Read this section alongside the surrounding pages in Recurring Decimals. That gives you the full topic sequence instead of a single isolated revision point.

Notation Worked Example 1: Simple Recurring Decimals That Never End Worked Example 2: Two-Digit Recurring

Practice Questions for Recurring Decimals

Which of these fractions gives a recurring decimal when you divide?

A. 1/3
B. 1/4
C. 3/5
D. 7/8

1 markfoundation

Explain why 1/6 gives a recurring decimal. You must refer to prime factors in your answer.

3 markschallenge

Quick Recall Flashcards

What is a recurring decimal?

A decimal where one or more digits repeat infinitely in a regular pattern. Examples: 0.333... = 1/3, 0.090909... = 1/11

What does dot notation mean in recurring decimals?

A dot above a single digit: that digit repeats. 0.3̇ = 0.333... Dots above two digits: the entire block between them repeats. 0.1ї8ї = 0.181818...

14 questions on Recurring Decimals — practise free

Instant marking, adaptive difficulty, and 11 spaced repetition flashcards. Free until your GCSEs.

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Notation

Worked Example 1: Simple Recurring