# How do you multiply scientific notation (0.33 x 10^ -3) x (0.2 x 10)?

Mar 12, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(0.33 \times 0.2\right) \times \left({10}^{-} 3 \times 10\right) \implies$

$0.066 \times \left({10}^{-} 3 \times {10}^{1}\right)$

Next, use this rule of exponents to multiply the 10s terms:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$0.066 \times \left({10}^{\textcolor{red}{- 3}} \times {10}^{\textcolor{b l u e}{1}}\right) \implies$

$0.066 \times {10}^{\textcolor{red}{- 3} + \textcolor{b l u e}{1}} \implies$

$0.066 \times {10}^{-} 2$

To write this in scientific notation we must move the decimal point 2 places to the left so we need to subtract 2 from the 10s exponent:

$0.066 \times {10}^{-} 2 \implies$

$6.6 \times {10}^{-} 4$