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Rational Number - GCSE Maths Definition

Reviewed by: Roger B

Last updated

14 May 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

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