IRRATIONAL NUMBER Definition & Meaning

irrational number

noun

Mathematics.

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

irrational number

noun

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

irrational number

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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

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

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Notes

The square roots of most whole numbers are irrational numbers.

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�y��vlog History and Origins

Origin of irrational number¹

First recorded in 1545–55

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Example Sentences

Examples have not been reviewed.

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.

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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.

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

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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.

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

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