\begin{definition}[Definition:General Logarithm/Common/Mantissa]
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 $d$
: $m := \log_{10} a$
$\log_{10} a$ is the '''mantissa''' of $\log_{10} n$.
\end{definition}