# irrational number

CEFR B2 · Compound

Source: https://englishreference.com/word/irrational-number
Updated: 2026-08-05

## Definition

a number that cannot be written as a simple fraction because its decimals go on forever without repeating a pattern.

For teachers: a real number that cannot be expressed as a ratio of two integers. Its decimal expansion is non-terminating and non-recurring.

## Examples

- Pi is the most famous irrational number.
- In math class, we learned that the square root of two is an irrational number.
- The discovery of irrational numbers challenged the ancient Pythagorean belief that all things in the universe could be measured by whole numbers and their ratios.

## Usage notes

- primarily used in mathematical and scientific contexts.
- Teaching tip: contrast with 'rational number' (which can be a fraction); use the number Pi as a concrete anchor for students to visualize the infinite, non-repeating decimal.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.