# irrational number

### noun Mathematics.

a number that cannot be exactly expressed as a ratio of two integers.

## RELATED CONTENT

## Nearby words

- irradiant,
- irradiate,
- irradiation,
- irradicable,
- irrational,
- irrationalism,
- irrationality,
- irrationalize,
- irrawaddy,
- irreal

## Origin of irrational number

First recorded in 1545–55

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

## irrational number

### noun

any real number that cannot be expressed as the ratio of two integers, such as π

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

## irrational number

[ ĭ-răsh′ə-nəl ]

A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (√2) are irrational numbers.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

## irrational number

A number that cannot be expressed as the ratio of two whole numbers.

## Note

The square roots of most whole numbers are irrational numbers.

The New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.