Number

Irrational number

A number that cannot be written as a fraction of two integers — its decimal goes on forever without repeating.

Definition

Irrational numbers include surds like √2 and constants like π. Their decimal expansions never terminate and never settle into a repeating pattern.

Example

√2, √3, π, e are all irrational.

Related terms

Rational number

A number you can write as a fraction p/q where p and q are integers and q ≠ 0.

Surd

An irrational root that cannot be simplified to a rational number, e.g. √2, √15.

Practise GCSE Maths topics with instant examiner-style marking — every term in context.