# Math Help - [SOLVED] Need help with one thing

1. ## [SOLVED] Need help with one thing

i dont know what to do with the number 3.2 in this problem trying to obtian the loudness of a sound in decibals. I already did some of the steps

$10log(3.2* 10^{-5}W/m^{2}-10^{-12}W/m^{2})$ I just dont know what to do with the 3.2 in the equation. Only have done problems that use $1.0* 10^{n}$ And with 1.0 the answer would be $10^{7}$ or 70 dB

2. $3.2\cdot 10^{-5}\;-\;1.0\cdot 10^{-12}$

$\;=\;32000000\cdot 10^{-12}\;-\;1.0\cdot 10^{-12}$

$\;=\;31999999\cdot 10^{-12}$

Where does that leave us?

Of course, someone is going to worry about significant digits. Subtracting with 7 orders of magnitude difference is a touchy subject. With a few more orders of magnitude, I like this explanation:

Weight of the Earth + Grain of Sand = Weight of the Earth