irrational number

American  

noun

Mathematics.

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

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irrational number British  

noun

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

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irrational number Scientific  

/ ĭ-răsh′ə-nəl /

1. 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.

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irrational number Cultural  

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

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Discover More

The square roots of most whole numbers are irrational numbers.

Etymology

Origin of irrational number

First recorded in 1545–55

Example Sentences

Pi has fascinated mathematicians for thousands of years, not least because it is an irrational number — its digits seem to go on forever without falling into a repeating pattern, a tantalizing glimpse of infinity.

From New York Times • Mar. 13, 2024

The baby boy’s nickname, Tau, was inspired by “the Greek letter representing the irrational number that is equal to two times pi,” the biography explains.

From Los Angeles Times • Sep. 10, 2023

In this way, an irrational number with an infinite number of decimal places will be obtained.

From Scientific American • Jul. 13, 2023

Pi Gaslight: A promising mathematician is almost driven mad by her jealous husband when he insists there is no such thing as an irrational number.

From Washington Post • Nov. 3, 2022

To add insult to injury, the Pythagoreans soon discovered that the golden ratio, the ultimate Pythagorean symbol of beauly and rationality, was an irrational number.

From "Zero: The Biography of a Dangerous Idea" by Charles Seife