What is Irrational Number? Definition, Meaning & Example
A number that cannot be expressed as a fraction p/q with integer values, and has a non-repeating, non-terminating decimal expansion.
TL;DR: A number that cannot be expressed as a fraction p/q with integer values, and has a non-repeating, non-terminating decimal expansion.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Irrational Number: A number that cannot be expressed as a fraction p/q with integer values, and has a non-repeating, non-terminating decimal expansion.
Explanation
Irrational numbers cannot be written as exact fractions but can only be approximated. Common examples include pi (approximately 3.14159...) and the square root of 2 (approximately 1.414...). The number pi is fundamental in geometry for calculating circle properties. The square root of 2 appears frequently in geometry and is the first number historically proven to be irrational. Irrational numbers, combined with rational numbers, form the set of real numbers. Most numbers involving square roots, cube roots, and transcendental numbers are irrational.
Example
Pi is an irrational number approximately equal to 3.14159265... The digits continue forever without repeating, so pi cannot be expressed as a simple fraction.
Frequently Asked Questions
How do you know a number is irrational?
If a number cannot be expressed as p/q (fraction) and its decimal expansion never repeats or terminates, it is irrational.
Is the square root of 4 irrational?
No, the square root of 4 equals 2, which is a rational number (integer). Only square roots of non-perfect squares are irrational.
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