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Decimals That Never End
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.
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
Mathematics glossary
- 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...
Notation
A dot over a single digit means that digit repeats. Dots over two digits means those two digits repeat together.
Now try it yourself
Quiz · Question 1 of 14
Which of these fractions gives a recurring decimal when you divide?
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This topic in real past papers
Every real exam question we've found on recurring decimals, with a full worked answer.