This key facts covers Notation 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 2 of 6 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Notation
| Decimal | Meaning | Fraction |
|---|---|---|
| 0.3̇ | 0.333333... | 1/3 |
| 0.1̇2̇ | 0.121212... (12 repeats) | 12/99 = 4/33 |
| 0.16̇ | 0.1666... (only 6 repeats) | 1/6 |
A dot over a single digit means that digit repeats. Dots over two digits means those two digits repeat together.
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 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...
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