How to Use irrational number in a Sentence

irrational number

noun
  • Pi is an irrational number — it cannot be expressed as a fraction.
    — Becky Krystal, Washington Post, 12 Mar. 2026
  • Pi is an irrational number, meaning that it cannot be expressed as a simple fraction.
    — Avery Hurt, Discover Magazine, 14 Mar. 2021
  • An irrational number is one that cannot be expressed by a fraction of integers, or whole numbers.
    — Jay Bennett, Popular Mechanics, 11 May 2018
  • But no matter how fine the grid, the ninth dot always falls between grid points; it is forced to correspond to an irrational number.
    — Quanta Magazine, 22 Sep. 2015
  • With an irrational number, those nested layers will go on forever.
    — Popular Mechanics, 21 Feb. 2021
  • Many people may have an irrational number in mind, such as pi (π), Euler’s number (e) or the square root of 2.
    — Manon Bischoff, Scientific American, 3 Mar. 2023
  • And on this day, math enthusiasts around the world celebrate the irrational number.
    — Francisco Guzman and Saeed Ahmed, CNN, 14 Mar. 2020
  • This distinguishes it again from more familiar irrational numbers like the square root of two (whose second power is equal to two).
    — Dan Rockmore /, NBC News, 14 Mar. 2018
  • Math enthusiasts and plenty of students know all about the day that celebrates the irrational number that never ends.
    — Alexandra Meeks, CNN, 13 Mar. 2022
  • For every irrational number α, there are infinitely many fractions p⁄q.
    — Manon Bischoff, Scientific American, 19 June 2026
  • Next, choose two angle measurements that are an irrational number of degrees (that is, any number of degrees, like pi, that can’t be written as a fraction).
    — Quanta Magazine, 26 Aug. 2021
  • For the math-averse, pi is an irrational number (as in can’t be represented by a fraction) used in geometry formulas, such as the area of a circle.
    — Aaron Hutcherson, Washington Post, 13 Mar. 2023
  • The vast majority are irrational numbers, never-ending decimals that cannot be written as fractions.
    — Wired, 18 Aug. 2019
  • Making matters worse, the golden ratio is another irrational number!
    — Steven Salzberg, Forbes, 18 Apr. 2022
  • The larger the denominators of the fractions used, the smaller the difference to the irrational number.
    — Manon Bischoff, Scientific American, 19 June 2026
  • Real examples and applications are messy, with ugly roots made of decimals or irrational numbers.
    — Caroline Delbert, Popular Mechanics, 6 Dec. 2019
  • His name is Techno Mechanicus Musk, but his parents call him Tau, for the irrational number.
    — Jill Lepore, The New Yorker, 11 Sep. 2023
  • The short way to say this is that pi is an irrational number, one that cannot be represented as a fraction and thus has an infinite and never-repeating decimal expansion.
    — Dan Rockmore /, NBC News, 14 Mar. 2018
  • So the aim for experts is to try to create a larger denominator to improve the fraction’s ability to approximate an irrational number.
    — Manon Bischoff, Scientific American, 19 June 2026
  • Pi itself is an irrational number with a decimal representation that goes on forever without a repeating pattern.
    — Rick Mauch, Fort Worth Star-Telegram, 24 Sep. 2025
  • But instead the vectors had a ratio of the square root of 2—definitely an irrational number—showing that the polyiamond arrangements weren’t periodic.
    — Manon Bischoff, Scientific American, 10 Apr. 2023
  • In 1837 the mathematician Gustav Lejeune Dirichlet found a rule for how well irrational numbers can be approximated by rational ones.
    — Wired, 18 Aug. 2019
  • The special occasion was first commemorated back in 1988, when physicist Larry Shaw organized the holiday in San Francisco to honor the infinite, irrational number that has been utilized in mathematics and science for thousands of years.
    — Dave Quinn, PEOPLE.com, 8 Mar. 2022

Some of these examples are programmatically compiled from various online sources to illustrate current usage of the word 'irrational number.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

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