Mantissa

Mantissa is a term used in two related contexts in mathematics and computing. In the study of logarithms, the mantissa is the fractional part of a logarithm expressed in a fixed base. In modern computing, the term most often refers to the significand, the part of a floating-point number that contains its significant digits.

For a positive number x, log_b(x) can be written as n + m, where n is the integer part and m is the mantissa with 0 ≤ m < 1 (in common base-10 notation). The mantissa encodes the scale-free digits of x and was historically used in logarithmic tables to interpolate values.

In floating-point representation, numbers are typically written as ± m × b^e, where e is the exponent and m (the mantissa or significand) contains the significant digits. In normalized form, m lies in [1, b) (or [1, 2) in binary formats). The precision of the number is determined by the length of m, while the exponent controls its scale.

Terminology varies. Many computer scientists prefer significand for the floating-point quantity to avoid confusion with the logarithmic meaning of mantissa. Regardless of terminology, the mantissa carries the precision of a number, while the exponent scales it.