irrational number

noun

, Mathematics.

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

irrational number

noun

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

irrational number

/ 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.

irrational number

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

Notes

The square roots of most whole numbers are irrational numbers.

Word History and Origins

Origin of irrational number¹

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

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

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

From Scientific American

Eventually she leads us toward more abstract concepts such as the polar coordinate system, a graphical approach to defining a point using distance and angle, as well as irrational numbers and decimals that repeat infinitely.

From Scientific American

The real numbers are made up of the rational and irrational numbers.

From Scientific American