Definition:General Logarithm/Common/Mantissa

Definition
Let $n \in \R$ be a positive real number such that $0 < n < 1$.

Let $n$ be presented (possibly approximated) in scientific notation as:
 * $a \times 10^d$

where $d \in \Z$ is an integer.

Let $\log_{10} n$ be expressed in the form:
 * $\log_{10} n = \begin {cases} c \cdotp m & : d \ge 0 \\ \overline c \cdotp m & : d < 0 \end {cases}

where:
 * $c = \size d$ is the absolute value of $d$
 * $m := \log_{10} a$

Then $\log_{10} a$ is the mantissa of $\log_{10} n$.