Irrational Number

An irrational number is real number that cannot be expressed as a ratio of two integers. When an irrational number is written with a decimal point, the numbers after the decimal point continue infinitely with no repeatable pattern.

The number "pi" or π (3.14159...) is a common example of an irrational number since it has an infinite number of digits after the decimal point. Many square roots are also irrational since they cannot be reduced to fractions. For example, the √2 is close to 1.414, but the exact value is indeterminate since the digits after the decimal point continue infinitely: 1.414213562373095... This value cannot be expressed as a fraction, so the square root of 2 is irrational.

As of 2018, π has been calculated to 22 trillion digits and no pattern has been found.

If a number can be expressed as a ratio of two integers, it is rational. Below are some examples of irrational and rational numbers.

  • 2 - rational
  • √2 - irrational
  • 3.14 - rational
  • π - irrational
  • √3 - irrational
  • √4 - rational
  • 7/8 - rational
  • 1.333 (repeating) - rational
  • 1.567 (repeating) - rational
  • 1.567183906 (not repeating) - irrational

NOTE: When irrational numbers are encountered by a computer program, they must be estimated.

Updated June 5, 2018

Definitions by TechTerms.com

The definition of Irrational Number on this page is an original TechTerms.com definition. If you would like to reference this page or cite this definition, you can use the green citation links above.

The goal of TechTerms.com is to explain computer terminology in a way that is easy to understand. We strive for simplicity and accuracy with every definition we publish. If you have feedback about the Irrational Number definition or would like to suggest a new technical term, please contact us.

Want to learn more tech terms? Subscribe to the daily or weekly newsletter and get featured terms and quizzes delivered to your inbox.

Sign up for the free TechTerms Newsletter

How often would you like to receive an email?

You can unsubscribe or change your frequency setting at any time using the links available in each email.

Questions? Please contact us.