Difference between revisions of "Irrational number"
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| − | An '''irrational number''' is a number that cannot be expressed as the ratio of two [[integers | + | 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 | + | 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 (…): | ||
:<math>\pi\ = 3.1415926...</math> | :<math>\pi\ = 3.1415926...</math> | ||
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==See also== | ==See also== | ||
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[[Transcendental numbers]] | [[Transcendental numbers]] | ||
| − | [[Category: | + | [[Category:Mathematics]] |
Latest revision as of 14:27, July 13, 2016
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 (…):
- <math>\pi\ = 3.1415926...</math>