How do you evaluate (5.18times10^2)(9.1times10^-5)?

Jul 18, 2017

$0.047138$

Explanation:

$\left(5.18 \times {10}^{2}\right) \left(9.1 \times {10}^{-} 5\right)$

$\therefore {a}^{-} 5 = \frac{1}{a} ^ 5$

$\therefore = \left(5.18 \times 100\right) \left(\frac{9.1}{10} ^ 5\right)$

$\therefore = 518 \times \frac{9.1}{100000}$

$\therefore = 518 \times 0.00091$

$\therefore = 0.047138$

Jul 18, 2017

$4.7138 \times {10}^{- 2}$

Explanation:

Lets get rid of all the decimal places and put them back at the end.

$5.18 \times {10}^{2} = 518$

$9.1 \times {10}^{- 5} = 91 \times {10}^{- 6}$

So now we have: $518 \times 91 \times {10}^{- 6} \leftarrow \text{ "10^(-6)" is the same as } \frac{1}{10} ^ 6$

For the moment disregard the ${10}^{- 6}$

$\textcolor{w h i t e}{00} 518$
$\underline{\textcolor{w h i t e}{000} 91} \leftarrow \text{ Multiply}$
$\textcolor{w h i t e}{0} 4662 \leftarrow 518 \times 90$
$\underline{\textcolor{w h i t e}{00} 518} \leftarrow 518 \times 1$
$47138 \leftarrow 4662 + 518$

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Now we put back the $\times \frac{1}{10} ^ 6$

$47138 \times \frac{1}{10} ^ 6 \text{ "=" } 0.047138$

Writing this in the same format as in the question (a good move)

$4.7138 \times \frac{1}{10} ^ 2 \text{ "->" } 4.7138 \times {10}^{- 2}$