Rational number

In mathematics, a rational number (or informally fraction) is a ratio or quotient of two integers, usually written as the vulgar fraction a/b, where b is not zero.

Related Topics:
Mathematics - Fraction - Ratio - Integers - Vulgar fraction - Zero

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Each rational number can be written in infinitely many forms, for example 3/6 = 2/4 = 1/2. The simplest form is when a and b have no common divisors, and every non-zero rational number has exactly one simplest form of this type with positive denominator.

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The decimal expansion of a rational number is eventually periodic (in the case of a finite expansion the zeroes which implicitly follow it form the periodic part). The same is true for any other integral base above 1. Conversely, if the expansion of a number for one base is periodic, it is periodic for all bases and the number is rational.

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A real number that is not rational is called an irrational number.

Related Topics:
Real number - Irrational number

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In mathematics, the term "rational something" means that the underlying field considered is the field mathbb{Q} of rational numbers. For example, rational polynomials or rational prime ideals.

Related Topics:
Field - Polynomial - Prime ideal

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The set of all rational numbers is denoted by Q, or in blackboard bold mathbb{Q}. Using the set-builder notation mathbb{Q} is defined as such:

Related Topics:
Set - Blackboard bold - Set-builder notation

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:mathbb{Q} = left{rac{m}{n} : m in mathbb{Z}, n in mathbb{Z}, n e 0 ight}

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