1 รท 3 = 0.333333... it goes on forever! We write this as 0.3ฬ (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.
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.
Practice questions for Recurring Decimals
Which of these fractions gives a recurring decimal when you divide?
Explain why 1/6 gives a recurring decimal. You must refer to prime factors in your answer.
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. 0.3ฬ = 0.333...
Dots above two digits: the entire block between them repeats. 0.1ั8ั = 0.181818...