NumberIntroduction

Decimals That Never End

Part of Recurring DecimalsGCSE Mathematics

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 5 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 5

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.
Recurring decimals diagram

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.

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...

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