NumberIntroduction

Decimals That Never End

Part of Recurring Decimals · GCSE GCSE Mathematics revision

This introduction covers Decimals That Never End 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 1 of 6 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 6

Practice

14 questions

Recall

11 flashcards

Decimals That Never End

1 ÷ 3 = 0.333333... it goes on forever! We write this as 0.3̇ (with a dot over the 3). But here's the amazing thing: these infinite decimals are actually exact fractions in disguise. Learning to convert between them is a key Higher tier skill.

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 Converting Recurring Decimal → Fraction Worked Example 1: Simple 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

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Recurring Decimals

Notation