# How do you simplify (2.135times10^5)/(3.5times10^12)?

Feb 16, 2017

$6.1 \times {10}^{- 8}$

#### Explanation:

$2.135 \times {10}^{5} = 213500$

$3.5 \times {10}^{12} = 3500000000000$

then you are able to do the calculation (use a calculator).The calculator gives the answer of

$0.000000061 = 6.1 \times {10}^{- 8}$

Feb 16, 2017

This is a sort of cheat method to make the numbers easier to deal with.

$6.1 \times {10}^{- 8}$

#### Explanation:

Given: $\frac{2.135 \times {10}^{5}}{3.5 \times {10}^{12}}$

but $2.135 \times {10}^{5}$ is the same as $2135 \times {10}^{2}$
and $3.5 \times {10}^{12}$ is the same as $3500 \times {10}^{9}$

and ${10}^{2} / {10}^{9} = {10}^{2} / \left({10}^{2} \times {10}^{7}\right) = \frac{1}{10} ^ 7$

$\textcolor{w h i t e}{.}$
$\textcolor{w h i t e}{.}$

So we now have:

$\frac{2135}{3500} \times \frac{1}{10} ^ \left(7\right)$

$\frac{2135 \div 5}{3500 \div 5} \times \frac{1}{10} ^ \left(7\right) \text{ "=" } \frac{427}{700} \times \frac{1}{10} ^ 7$

$\text{ "=" } \frac{427}{7} \times \frac{1}{10} ^ 9$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using long division $427 \div 7$ is:

$\text{ } 427$
$\textcolor{red}{60} \times 7 \to \underline{420} \leftarrow \text{ subtract}$
$\text{ } \textcolor{w h i t e}{42} 7$
$\textcolor{w h i t e}{6} \textcolor{red}{1} \times 7 \to \underline{\textcolor{w h i t e}{42} 7} \leftarrow \text{ subtract}$
$\text{ } 0$

$427 \div 7 \text{ is: } \textcolor{red}{60 + 1} = 61$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So $\text{ "427/7xx1/10^9" "=" "61xx1/10^9" "=" } 6.1 \times \frac{1}{10} ^ 8$

Which is the same as: $\text{ } 6.1 \times {10}^{- 8}$