# Question db6ff

Jan 19, 2017

$0.000665 = 6.65 \times {10}^{- 4}$

#### Explanation:

$\textcolor{b l u e}{\text{Principle used}}$

Consider the number 2. If you multiply by 1 you do not change its value. However, 1 comes in many forms. So you can change the way it looks without changing its true value

color(green)([2color(red)(xx1)] -=[2color(red)(xx10/10)] =[20xx1/10]#

But $\frac{1}{10}$ is the same as ${10}^{- 1}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$0.000665 \to 0.0065 \times \frac{1}{10}$
$0.000665 \to 0.065 \times \frac{1}{10} \times \frac{1}{10}$
$0.000665 \to 0.65 \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}$
$0.000665 \to 6.5 \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10}$

but $\frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} \times \frac{1}{10} = \frac{1}{{10}^{4}} = {10}^{- 4}$

So $0.000665 = 6.65 \times {10}^{- 4}$