irrational number

A real number that cannot be expressed as a ratio between two integers.

American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

irrational number

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

Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

irra′tional num′ber

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

[1545–55]

ir·ra·tion·al number

(ĭ-răsh′ə-nəl)

A real number that cannot be expressed as a ratio between two integers. 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® Student Science Dictionary, Second Edition. Copyright © 2014 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

ThesaurusAntonymsRelated WordsSynonymsLegend:

Noun

irrational number - a real number that cannot be expressed as a rational number

irrational

real, real number - any rational or irrational number

transcendental number - an irrational number that is not algebraic

algebraic number - root of an algebraic equation with rational coefficients

Translations

άρρητος αριθμός

número irracional

irrationaaliluku

iracionalni broj

óræð tala

Mentioned in

References in periodicals archive

"We didn't want to set another irrational number," he says.

Bloody dilemma

Mathematicians, for instance, provedlong ago that pi is an irrational number. This means that it takes a never-ending string of digits to express pi as a decimal number.

Pi wars: dueling with supercomputers

Instead, the irrational number, (1 + [square root of] 5)/2, pervades the pattern.

The fivefold way for crystals

Pi represents an irrational number that begins with 3.141592653 and continues indefinitely.

It Is Pi (Pie) Day Today!

Mathematicians everywhere will testify that Pi is a wonderful, never-ending irrational number which makes it the most fascinating number in world mathematics 3.1415926535 ..

It's only a number - but Pi Day gives the world a taste of the infinite sum; THE FACT MASTER KNOWS WHAT HAPPENED AND WHEN

That pi's digits continue to infinity without pattern or termination is at once pedestrian - the same is true of any irrational number in our decimal system, after all - and undeniably fascinating.

Cinema Science: PI AND THE RAPTURE OF COMPLEX MATHEMATICS: While its title already indicates one of its central mathematical topics of concern, Darren Aronofsky's cult paranoid thriller also offers ample prompts for senior secondary students to explore sequences, phenomena such as the golden ratio and Pythagoras' theorem, and more intricate concepts like irrational numbers and recursion, as DAVE CREWE outlines

Finite continued fractions represent always rational numbers, whereas infinite continued fractions represent irrational numbers. That is why any irrational number can be approximated by finite continued fractions--the convergents which deliver always the best and quickest approximation [11].

Global Scaling of Planetary Systems

Coincidentally, the Carbondale sectional was held on "Pi Day," or March 14, so called because the first three numbers of the date are "3-14" like the irrational number pi (3.14).

WYSE team wins sectional, will compete in state championship in April WYSE

In this section, we begin with an irrational number [[omega].sub.0] [member of] [0,1[ and a partition of [0,1] into l [less than or equal to] d subintervals with the requirement that one of the interior nodes is 1- [[omega].sub.0]:

The Existence and Structure of Rotational Systems in the Circle

Pi, the ratio of a circle's circumference to its diameter, is an irrational number that extends to trillions of digits beyond the decimal point.

Find your birthday in Pi's first 200 million digits

In particular, an irrational number is a Liouville number if and only if it is not Diophantine.

On variations of the Liouville constant which are also Liouville numbers

They realised that [empty set] was an irrational number and embodied it in the pentagram, which they used as their secret sign.

The pentagon