Question

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

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(0.33 xx 0.2) xx (10^-3 xx 10) =>`

`0.066 xx (10^-3 xx 10^1)`

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

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`0.066 xx (10^color(red)(-3) xx 10^color(blue)(1)) =>`

`0.066 xx 10^(color(red)(-3)+color(blue)(1)) =>`

`0.066 xx 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 xx 10^-2 =>`

`6.6 xx 10^-4`