Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Description
Since q may be equal to 1, every integer is a rational number.
The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold \mathbb{Q}, Unicode ℚ); it was thus denoted in 1895 by Peano after quoziente, Italian for "quotient".
The decimal representation of a rational number always either terminates after a finite number of digits, or begins to repeat the same finite sequence of digits over and over.
Conversely, any repeating or terminating decimal represents a rational number.
These statements hold true not just for base 10, but also for any other integer base (e.g. binary, hexadecimal).
Irrational numbers
A real number that is not rational is called an irrational number, or simply irrational.
The decimal expansion of an irrational number continues without repeating.
Irrational numbers include √2, π, e, and φ.
See also
- Decimal representation
- Floating point
- Ford circles
- Integer
- Mathematics
- Niven's theorem
- Number
- Rational data type
External links
- Rational number @ Wikipedia
