# How do you write the answer in scientific notation given ((3.3times10^9)(2.8times10^-7))/(4.62times10^5)?

Mar 21, 2017

$2.0 \times {10}^{- 3}$

#### Explanation:

We do this in 3 parts:

The numbers

The powers of 10

The final adjustment so that there is only 1 digit to the left of the decimal point and that that digit is greater than 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 1}}$

$\frac{3.3 \times 2.8}{4.62} = 2.0$

Note that step 3 not needed as there is only 1 digit non zero to right of decimal point.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Step 2}}$

Note that ${10}^{- 7} \to \frac{1}{10} ^ 7$

${10}^{9} \times \frac{1}{10} ^ 7 \times \frac{1}{10} ^ 5 = {10}^{9} / {10}^{12} = {10}^{9 - 12} = {10}^{- 3}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$2.0 \times {10}^{- 3}$

Mar 21, 2017

Igot: $2 \times {10}^{-} 3$

#### Explanation:

We can deal first with the powers of ten using the rule of exponents to get:
${10}^{9} \cdot {10}^{-} \frac{7}{10} ^ 5 = {10}^{9 - 7} / {10}^{5} = {10}^{2 - 5} = {10}^{-} 3$
next we deal with the numbers:
$3.3 \times 2.8 = 9.24$
and
$\frac{9.24}{4.62} = 2$

so that we get:
$2 \times {10}^{-} 3$