A real number that cannot be expressed as the ratio of two integers. Examples of irrational numbers are the square root of 3, pi, and e. See also integer, real number.
A real number that cannot be expressed as a rational number.
A number that cannot be expressed as an exact fraction. Irrational numbers include some square roots (for example, Ö12, Ö13, and Ö 15 are irrational) and numbers such as p (the ratio of the circumference of a circle to its diameter, which is approximately equal to 3.14159) and e (the base of natural logarithms, approximately 2.71828).