A rational number is one which can be expressed as the ratio of two integers such as 3/4 (the ration of 3 to 4) or -5: 10 (the ration of -5 to 10). Among the infinitely many rational numbers are 1.345, 1 7/8, 0, -75, 25, .125, and 1. These numbers are rational because they can be expressed as 1345:1000, 15:8, 0:1, -75:1, 5:1, 1:2, and 1:1 respectively. The numbers , 2, i, and 4 are not rational because none of them can be written as the ratio of two integers. Thus any integer, any common fraction, any mixed number, any finite decimal, or any repeating decimal is rational. A rational number that is the ratio of a to b is usually written as the fraction a/b.

Rational numbers are needed because there are many quantities or measures which natural numbers or integers alone will not adequately describe. Measurement of quantities, whether length, mass, or time, is the most common situation. Rational numbers are needed, for...