# About how many times less than 5times10^7 is 4times10^5?

Jan 1, 2017

$4 \times {10}^{5} \text{ is "color(red)(1.25xx10^2)" times less than } 5 \times {10}^{7}$

"That is: "color(green)(" (4xx10^5)xxcolor(red)((1.25xx10^2))=5xx10^7)

#### Explanation:

In the question is the word 'times'. This point to a multiplication.

Let the unknown constant of conversion be $k$

Then we have:

$\textcolor{g r e e n}{5 \times {10}^{7} = \left(4 \times {10}^{5}\right) \times k}$

$k = \frac{5 \times {10}^{7}}{4 \times {10}^{5}}$

$k = \frac{5 \times \cancel{{10}^{5}} \times {10}^{2}}{4 \times \cancel{{10}^{5}}}$

$k = \frac{5}{4} \times {10}^{2}$

But $\frac{5}{4} = 1 \frac{1}{4} = 1.25$ giving:

$k = 1.25 \times {10}^{2}$