Dealing with US Dollars...
Assuming we know the weights of half-dollars, quarters, dimes, nickels, and pennies.
Also assuming the weights remain constant (don't change from one quarter to another quarter).
If we have a bag of these coins (could include any coin), and we weigh them to get a total weight, can we know how much money we have in the bag?
If we cannot know exactly, how close of an estimate can we get?
According to the U.S. Mint, nickels weigh 5.000 grams and pennies 2.500 grams. So you generally cannot know exactly how much money is in the bag: for example, 10 grams of coins could be two nickels (10 cents) or four pennies (4 cents).
http://www.usmint.gov/about_the_mint/?action=coin_specifications