In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers.

Irrational numbers cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.

When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common.

Numbers which are irrational include the ratio π of a circle's circumference to its diameter, Euler's number e, the golden ratio φ, and the square root of two.

All square roots of natural numbers, other than of perfect squares, are irrational.

**Source adapted from** Irrational number. (2015, August 26). In Wikipedia, The Free Encyclopedia. Retrieved 10:31, August 26, 2015, from https://en.wikipedia.org/w/index.php?title=Irrational_number&oldid=677860905