# How do you simplify (1.8times10^-3)/(9times10^2) in scientific notation?

Mar 22, 2016

$2 \times {10}^{- 6}$

#### Explanation:

Given:$\text{ } \frac{1.8 \times {10}^{- 3}}{9 \times {10}^{2}}$..................(1)

If we can change the 1.8 so that it looks like 18 then $\frac{18}{9} = 2$

$1.8 \text{ is the same as } \frac{18}{10}$

and $\frac{18}{10} \text{ is the same as } 18 \times {10}^{- 1}$

So rewrite expression (1) as$\text{ " (18xx10^(-1)xx10^(-3))/(9xx10^2)" } \ldots \left({1}_{a}\right)$

Note that $\text{ } \frac{1}{10} ^ 2$ is the same as$\text{ } {10}^{- 2}$

So rewrite expression $\left({1}_{a}\right)$ as:

$\frac{18}{9} \times {10}^{- 1} \times {10}^{- 3} \times {10}^{- 2}$

Giving:$\textcolor{b l u e}{\textcolor{b r o w n}{\text{ } 2 \times {10}^{- 1 - 3 - 2}} = 2.0 \times {10}^{- 6}}$