# How do I solve 0.001 = "10,000,000"/y?

Apr 11, 2017

$y$ = 10,000,000,000

#### Explanation:

Since y is at the bottom of the fraction, it can switch place with the 0.001.

$y$ = $\frac{10 , 000 , 000}{0.001}$

$y$ = 10,000,000,000

Apr 11, 2017

Convert the numbers to powers of 10, and use the exponent laws: ${10}^{a} / {10}^{b} = {10}^{a - b} .$

$y = {10}^{10} = \text{10,000,000,000} .$

#### Explanation:

Let's rewrite this question using powers of 10:

$0.001 = \frac{\text{10,000,000}}{y}$

${10}^{\text{-3}} = \frac{{10}^{7}}{y}$

When we solve this for $y$, we get

$y = \frac{{10}^{7}}{10} ^ \text{-3}$

The exponent rules tell us that ${10}^{a} / {10}^{b}$ is equal to ${10}^{a - b}$. Using this, we get

y=(10^7)/10^"-3"=10^(7-("-3"))
$\textcolor{w h i t e}{y = \frac{{10}^{7}}{10} ^ \text{-3}} = {10}^{7 + 3}$
color(white)(y=(10^7)/10^"-3")=10^10" "="10,000,000,000"