Definition:Mantissa
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Definition
Scientific Notation
Let $n$ be a number expressed in scientific notation as:
- $n \approx m \times 10^e$
The number $m$ is known as the mantissa.
General Logarithm
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 $\log_{10} n$.