Home : Technical Terms : Irrational Number Definition

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

Cite this definition:


TechTerms - The Tech Terms Computer Dictionary

This page contains a technical definition of Irrational Number. It explains in computing terminology what Irrational Number means and is one of many technical terms in the TechTerms dictionary.

All definitions on the TechTerms website are written to be technically accurate but also easy to understand. If you find this Irrational Number definition to be helpful, you can reference it using the citation links above. If you think a term should be updated or added to the TechTerms dictionary, please email TechTerms!

Subscribe to the TechTerms Newsletter to get featured terms and quizzes right in your inbox. You can choose to receive either a daily or weekly email.

Sign up for the free TechTerms Newsletter

How often would you like to receive an email?

You can unsubscribe at any time.
Questions? Please contact us.