# How do you write 0.125 in scientific notation?

Aug 19, 2016

0.125 = color(green)(1.25xx10^(-1) ("normalized")

#### Explanation:

Numbers in scientific notation are written as the product of two components:
$\textcolor{w h i t e}{\text{XXX")"the "color(red)("mantissa}}$
and
$\textcolor{w h i t e}{\text{XXX")"10 to some integer "color(blue)("exponent}}$

In $\textcolor{g r e e n}{\text{normalized}}$ form, the $\textcolor{red}{\text{mantissa}}$ (unless zero) is written as a decimal fraction with exactly one non-zero digit before the decimal point.

Using a $\textcolor{red}{\text{mantissa}}$ of $\textcolor{red}{1.25}$
with an $\textcolor{b l u e}{\text{exponent}}$ of $\textcolor{b l u e}{2}$: $\textcolor{red}{1.25} \times {10}^{\textcolor{b l u e}{2}} = \textcolor{b r o w n}{125}$
with an $\textcolor{b l u e}{\text{exponent}}$ of $\textcolor{b l u e}{1}$: $\textcolor{red}{1.25} \times {10}^{\textcolor{b l u e}{1}} = \textcolor{b r o w n}{12.5}$
with an $\textcolor{b l u e}{\text{exponent}}$ of $\textcolor{b l u e}{0}$: $\textcolor{red}{1.25} \times {10}^{\textcolor{b l u e}{0}} = \textcolor{b r o w n}{1.25}$
with an $\textcolor{b l u e}{\text{exponent}}$ of $\textcolor{b l u e}{- 1}$: $\textcolor{red}{1.25} \times {10}^{\textcolor{b l u e}{- 1}} = \textcolor{b r o w n}{0.125}$ [$\textcolor{g r e e n}{\text{the value we wanted}}$]