# How do you evaluate (2.05times10^-8)/(4times10^-2)?

Apr 20, 2017

$= 5.125 \times {10}^{-} 7$

#### Explanation:

Do not be tempted to change the numbers into decimal notation - that defeats the purpose of using scientific notation in the first place.

Consider $\text{ } \frac{12 {x}^{-} 5}{4 {x}^{-} 3}$

This could be written as: $\frac{12 {x}^{- 5 - \left(- 3\right)}}{4}$

Simplifying leads to:$\text{ } 3 \times {x}^{-} 2 = \frac{3}{x} ^ 2$

In the same way " "(2.05 xx 10^-8)/(4 xx 10^-2

can be written as $\text{ } \frac{2.05 \times {10}^{- 8 - \left(- 2\right)}}{4}$

$= 0.5125 \times {10}^{-} 6$

Write in correct scientific notation - move the decimal place one place to the right the index will decrease.

$= 5.125 \times {10}^{-} 7$