Scientific Notation

Scientific notation is the expression of a number $n$ in the form $a\times 10^p$, where

$$p\equiv\left\lfloor{\log_{10}\vert n\vert}\right\rfloor$$

is the Floor of the base-10 Logarithm of $n$ (the ``order of magnitude''), and

$$a\equiv {n\over 10^p}$$

is a Real Number satisfying $1\leq \vert a\vert<10$. For example, in scientific notation, the number $n=101,325$ has order of magnitude

$$p=\left\lfloor{\log_{10} 101,325}\right\rfloor =\left\lfloor{5.00572}\right\rfloor =5,$$

so $n$ would be written $1.01325\times 10^5$. The special case of 0 does not have a unique representation in scientific notation, i.e., $0=0\times 10^0=0\times 10^1=\ldots$.

See also Characteristic (Real Number), Figures, Mantissa, Significant Digits