Rational number
A rational number is a number that can be expressed as the ratio of two integers.
Examples
- All integers are rational because every integer
can be represented as 
- Every number with a finite decimal expansion is rational (for example,
) - Every number with a periodic decimal expansion (for example, 0.314314314...) is also rational.
can be represented as 
)Moreover, any rational number in any base satisfies exactly one of the last two conditions.
Properties
- Rational numbers form a field. In plain English it means that you can add, subtract, multiply, and divide them (with the exception of division by
) and the result of each such operation is again a rational number. - Rational numbers are dense in the set of reals. This means that every non- empty open interval on the real line contains at least one (actually, infinitely many) rationals. Alternatively, it means that every real number can be represented as a limit of a sequence of rational numbers.
- Despite this, the set of rational numbers is countable, i.e. the same size as the set of integers.
) and the result of each such operation is again a rational number.See also
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