# How do you use scientific notation to compute products and quotients?

Mar 26, 2015

Scientific notation is of the form $a \cdot {10}^{n}$

What you do when you multiply is:
(1) you multiply the $a$'s
(2) you add the $n$'s (look at the signs!)

Example:
$\left(2.0 \cdot {10}^{3}\right) \cdot \left(1.55 \cdot {10}^{2}\right) = \left(2.0 \cdot 1.55\right) \cdot {10}^{3 + 2} = 3.1 \cdot {10}^{5}$

What you do when you divide is:
(1) you divide the $a$'s
(2) you subtract the $n$'s (look at the signs!)

Example:
$\frac{3.1 \cdot {10}^{5}}{2.0 \cdot {10}^{3}} = \left(\frac{3.1}{2.0}\right) \cdot {10}^{5 - 3} = 1.55 \cdot {10}^{2}$

Extra:
When there are negative signs in the exponents $n$ you proceed just the same, but you have to be more careful.