# How do you multiply (4.0 x 10^-5) * (3.1 x 10^-2)?

Apr 2, 2015

You can just multiply similars by similars, since there is only multiplication:

$\left(4.0 \cdot 3.1\right) \cdot \left({10}^{- 5} \cdot {10}^{- 2}\right)$

Exponents are added up if their base are the same and if they are multiplied.

$\left(12.4\right) \cdot {10}^{- 7}$

Second Way

The scientific notation is just there for readability.

The expression is equivalent to this:

$4 \cdot \left(\frac{1}{100000}\right) \cdot 3.1 \cdot \frac{1}{100}$

$= \frac{12.4}{10000000} = 12.4 \cdot {10}^{- 7}$