significand

The significand is the part of a number that encodes its significant digits. In many contexts it is also called the mantissa, though the term significand is preferred in modern mathematical and computing literature.

In decimal scientific notation, a real number is written as x = m × 10^e, where m is the significand and e is the exponent. The significand contains the significant digits and determines precision; the exponent merely scales the value.

In binary floating-point representations used by modern computers, a nonzero number is stored as x = (−1)^s × significand × 2^e. For normalized numbers the significand is in the interval [1, 2), typically written as 1.f where f is a fixed-length fractional part; the leading 1 is usually implicit and not stored, to maximize precision.

Subnormal (denormal) numbers relax normalization, allowing representation of values nearer to zero. When the exponent field is zero, the significand has no implicit leading 1 and is interpreted with a leading zero, enabling gradual underflow.

Precision and digits: the number of bits in the significand determines the precision of the representation. For a binary format with p significand bits, about p × log10(2) decimal digits are guaranteed. For example, binary32 uses 24 bits in the significand (including the implicit 1), about 7 decimal digits; binary64 uses 53 bits, about 15–16 digits.

Terminology notes: significand emphasizes the significant digits; mantissa is traditional in some texts, but significand is increasingly preferred to reduce confusion with logarithms.