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Scientific Notation

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

\begin{displaymath}
p\equiv\left\lfloor{\log_{10}\vert n\vert}\right\rfloor
\end{displaymath}

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

\begin{displaymath}
a\equiv {n\over 10^p}
\end{displaymath}

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

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

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




© 1996-9 Eric W. Weisstein
1999-05-26