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Rational Number - GCSE Maths Definition

Reviewed by: Roger B

Published

22 November 2024

Last updated

5 March 2025

What is a rational number?

A rational number is a number that can be written as a fraction, with an integer on the top of the fraction and an integer on the bottom of the fraction. For example, $\frac{3}{16}$ , $\frac{2}{7}$ and $\frac{1973}{877}$ are all rational numbers.

Integers are also rational numbers. Remember that an integer can always be written as a fraction over 1. For example, $5 = \frac{5}{1}$ .

The same definition also holds for negative numbers. For example, $- \frac{5}{8} = \frac{- 5}{8} = \frac{5}{- 8}$ is a rational number, as is $- 3 = \frac{- 3}{1} = \frac{3}{- 1}$ .

If a number is not rational, then it is irrational.

How can I tell if a decimal number is a rational number?

For a rational number, the decimal form of the number either terminates (ends), or is recurring (repeats forever in a pattern). For example:

$\frac{3}{16} = 0.1875$
- the decimal version ends at the 5
$\frac{2}{7} = 0 . \dot{2} 8571 \dot{4} = = 0.285714285714285714285714 . . .$
- the digits '285714' keep repeating forever

GCSE Maths Revision Resources to Ace Your Exams

To see more on rational and irrational numbers, read our revision notes on Types of Number. You can also have a go at our related exam questions. For quick-fire GCSE maths revision use our collection of interactive flashcards for GCSE maths. And don’t forget to check out the past papers for more general exam revision.

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