Irrational number

An irrational number is a real number that cannot be expressed as the ratio of two integers.

Irrational numbers often arise as solutions to problems involving rational numbers. For example, the square root of 2 is irrational. Other irrationals, such as pi, serve as fundamental constants in many mathematical problems.

Irrational numbers can never be expressed exactly using decimal notation with a finite number of digits. Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an ellipsis (…):

$\pi \ =3.1415926...$

See also

Transcendental numbers