How do you calculate (2.16times10^2) / (3times10^-4)?

Jun 15, 2017

It is $720 , 000$.

Explanation:

You can arrange your equation first:

$\frac{216}{0.0003}$

$= \frac{216 \times {10}^{4}}{3}$

$72 \times {10}^{4}$

or

$720 , 000$

$720 , 000$

Jun 15, 2017

divide the digits and then adjust the exponents

Explanation:

$\frac{2.16}{3} = 0.720$

$0.72 = 7.20 \times {10}^{-} 1$

$\frac{{10}^{-} 1 \times {10}^{2}}{10} ^ - 4 = {10}^{1} / {10}^{-} 4 = {10}^{5}$

the answer is $7.20 \times {10}^{5}$

Jun 15, 2017

See a solution process below:

Explanation:

First, rewrite this expression as:

$\left(\frac{2.16}{3}\right) \times \left({10}^{2} / {10}^{-} 4\right) \implies 0.72 \times {10}^{2} / {10}^{-} 4$

Now, use this rule of exponents to calculate the 10s terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$0.72 \times {10}^{\textcolor{red}{2}} / {10}^{\textcolor{b l u e}{- 4}} \implies 0.72 \times {10}^{\textcolor{red}{2} - \textcolor{b l u e}{- 4}} \implies 0.72 \times {10}^{\textcolor{red}{2} + \textcolor{b l u e}{4}} \implies$

$0.72 \times {10}^{6}$

To write this in proper scientific notation we need to move the decimal point 1 place to the right so we must subtract $1$ from 10s exponent:

$0.72 \times {10}^{6} \implies 7.2 \times {10}^{5}$