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. Instead it is common to write them using only enough significant digits to solve the problem at hand, followed by an | + | 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. | + | :<math>\pi\ = 3.1415926...</math> |
| − | == | + | ==See also== |
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[[Transcendental numbers]] | [[Transcendental numbers]] | ||
| − | [[ | + | |
| + | [[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>