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

An '''irrational number''' is a number that cannot be expressed as the ratio of two [[integers]].  Irrational numbers together with [[rational number]]s 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 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 (…):

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 (…):