# How do you write (3.00 times 10^8 m/s) / (5.68 times 10^9 m) in scientific notation?

Nov 5, 2015

The numbers are: $5.2817 \times {10}^{- 2}$
There is something wrong with the 'units' configuration in the question!!

#### Explanation:

First the numbers:

$\frac{3}{5.56} = .52817$ to 5 dp

write as
$5.2817 \times {10}^{- 1}$

Now look at the indices.

Note that ${10}^{- 1} = \frac{1}{10}$

$\frac{{10}^{8}}{10 \times {10}^{9}} = {10}^{- 2}$

Now look at the units:

$\frac{m}{s} \div i \mathrm{de} m = \frac{m}{s} \times \frac{1}{m} = \frac{1}{s}$

as it is one over s it is $\textcolor{b l u e}{\text{'per second' ( for each second)}}$

Putting it all together:

$5.2817 \times {10}^{- 2} \textcolor{red}{\text{(per second?????) that is can't be correct!!}}$
You have to have 'some form of unit' per second!!!!

Did you mean (m/s) divide (m/s) ?

If so then they all cancel out and you have no units. Just numbers!!