How to simplify  (7.1times10^-7)(8.6times10^-5) in scientific notation?

Jan 25, 2016

You multiply the numbers and add the 10-powers.

Explanation:

$= \left(7.1 \cdot 8.6\right) \cdot \left({10}^{- 7 - 5}\right)$
$= 61.06 \cdot {10}^{-} 12$

But we need to have only one digit in front of the decimal point:
$= \left(6.106 \cdot {10}^{1}\right) \cdot {10}^{-} 12 = 6.106 \cdot {10}^{1 - 12} = 6.106 \cdot {10}^{-} 11$

And, since the original numbers had only two significant digits, we will round this to $6.1 \cdot {10}^{-} 11$

Comment : I've placed brackets where they weren't technically necessary, but they may have added to the understanding of the steps we've taken.