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As it applies to general mathematics, a base is the number of single digits denoting different values in a positional numeral system, including zero. The decimal system uses base ten, hence the maximum number a single digit will ever reach is 9, after this it is necessary to add another digit to achieve a higher number.
Bases work using exponentiation. For example the decimal number 465 is represented by:
4 * 102 + 6 * 101 + 5 * 100, where 100 = 1.
This can be expanded for any integral or nonintegral number by using negative exponents (0.1 = 1 * 10-1).
See also: Numeral system.
Last updated: 02-24-2005 04:35:52