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Base (mathematics)
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Base (mathematics)

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:

+  + , where .

This can be expanded for any integral or nonintegral number by using negative exponents (0.1 = 1 * 10-1).

See also: Numeral system.