Irrational number

An irrational number is a number that cannot be expressed as the ratio of two integers. Irrational numbers together with rational numbers make up the set of real numbers.

Irrational numbers often arise as solutions to problems involoving 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. Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an elipsis:

<math>\pi\ = 3.14159...</math>

Formulations

An irrational number can be the limit of an infinite series of rational numbers.

See also

Transcendental numbers