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◉ Science·2 min·Updated Mar 12, 2026

What is Irrational Number?

Irrational Number

Quick Answer

An irrational number is a type of real number that cannot be expressed as a simple fraction. This means that its decimal representation goes on forever without repeating. Examples include numbers like pi and the square root of 2.

Overview

Irrational numbers are numbers that cannot be written as a fraction of two integers. This means that when you try to write them as a decimal, they will continue infinitely without repeating a pattern. For example, the number pi (approximately 3.14159) is irrational because it cannot be precisely expressed as a fraction, and its decimal form goes on forever without repeating. These numbers are important in mathematics because they help us understand the concept of real numbers, which include both rational and irrational numbers. Rational numbers can be expressed as fractions, while irrational numbers add depth to our number system. Understanding irrational numbers is essential for various mathematical concepts, such as geometry, where the length of the diagonal of a square is an irrational number, specifically the square root of 2. In real life, irrational numbers appear in many situations, such as in calculations involving circles. When measuring the circumference of a circle, we use pi, an irrational number. This shows how irrational numbers are not just theoretical but have practical applications in everyday life and various fields of science and engineering.

Frequently Asked Questions

Common examples of irrational numbers include pi (π) and the square root of 2. Both of these numbers cannot be expressed as a simple fraction and have non-repeating decimal expansions.
Rational numbers can be expressed as fractions, where both the numerator and denominator are integers. In contrast, irrational numbers cannot be written this way and have decimal representations that neither terminate nor repeat.
Irrational numbers are crucial for understanding the complete set of real numbers. They help in solving various mathematical problems, especially in geometry and calculus, where precise measurements often involve irrational values.