# How do you write (6 times 10^6) ÷ (8 times 10^3) in standard form?

May 21, 2018

$7.5 \times {10}^{2}$

#### Explanation:

If dividing a greater value into a lesser value is giving you a problem do this:

$6 \times {10}^{6} \text{ is the same as } 60 \times {10}^{5}$

So we have $\left(60 \times {10}^{5}\right) \div \left(8 \times {10}^{3}\right)$

$\frac{60}{8} \times {10}^{5} / {10}^{3}$

$\frac{60}{8} \times {10}^{5 - 3}$

$\frac{60}{8} \times {10}^{2}$
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By calculator we have: $7.5 \times {10}^{2}$
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I sort of cheat for the division $\frac{60}{8}$

$5 \times 8 = 40$ but to give us 60 we need 20 more.

Note that $\frac{1}{2}$ of $40 = 20$

$\textcolor{w h i t e}{\text{dddd")5xx8=40color(white)("dddd") -> color(white)("dddd}} 5 \times 8 = 40$
$\frac{1}{2} \times 5 \times 8 = \frac{1}{2} \times 40 \to \textcolor{w h i t e}{\text{ddd}} 2 \frac{1}{2} \times 8 = 20$

So $\underbrace{\left(2 \frac{1}{2} + 5\right)} \times 8 = 40 + 20 = 60$

$\textcolor{w h i t e}{\text{dddddd")7.5 color(white)("d}} \times 8 = 60$