In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero. Since b may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q

The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. (Our solved example in mathguru.com uses this concept).

These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.

The term rational in reference to the set Q refers to the fact that a rational number represents a ratio of two integers. In mathematics, the adjective rational often means that the underlying field considered is the field Q of rational numbers.

http://en.wikipedia.org/wiki/Rational_number

In mathematics, an irrational number is any real number which cannot be expressed as a fraction a/b, where a and b are integers, with b non-zero, and is therefore not a rational number. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are precisely those real numbers that cannot be represented as terminating or repeating decimals. (Our solved example in mathguru.com uses this concept).

 The best-known irrational numbers are π, e and √2.

http://en.wikipedia.org/wiki/Irrational_number

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