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:

<math>4*10^2<math> + <math>6*10^1<math> + <math>5*10^0<math>, where <math>10^0=1<math>.

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

See also: Numeral system.