How do you calculate 8 times10^6 ÷ 4 times 10^2?

May 8, 2016

$20 , 000 = 2 \times {10}^{4}$

Explanation:

First you put the numbers out of standard form:

${10}^{6} = 1 , 000 , 000$

$8 \times 1 , 000 , 000 = 8 , 000 , 000$

$4 \times {10}^{2} = 400$

Now the problem is like this:

8,000,000÷400

Cancel out some of the zeros so that the division is easier:

80,000÷4= 20,000

$= 2 \times {10}^{4}$

(Answers are generally given in the same form in which they are asked.)

May 8, 2016

$2 \times {10}^{4}$
(see below for possible alternative answer)

Explanation:

Assuming everything should be left in scientific notation
and that the expression was intended to be (not PEDMAS form)

$\textcolor{w h i t e}{\text{XXX}} \left(8 \times {10}^{6}\right) \div \left(4 \times {10}^{2}\right)$

$\textcolor{w h i t e}{\text{XXX}} = \frac{8}{4} \times \frac{{10}^{6}}{{10}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} = 2 \times {10}^{4}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Technically applying PEDMAS multiplication and division should be done in order from left to right.
So
$\textcolor{w h i t e}{\text{XXX}} 8 \times {10}^{6} \div 4 \times {10}^{2}$

$\textcolor{w h i t e}{\text{XXX}} = 8 , 000 , 000 \div 4 \times {10}^{2}$

$\textcolor{w h i t e}{\text{XXX}} = 2 , 000 , 000 \times {10}^{2}$

$\textcolor{w h i t e}{\text{XXX}} = 200 , 000 , 000$

$\textcolor{w h i t e}{\text{XXX}} = 2 \times {10}^{8}$

...however, I suspect the parenthesized version is what was intended.