Moneybags

Here are ten moneybags each filled with a large number of coins. (Some bags may contain more coins than others.) All the coins look exactly alike, but those in one of the bags are actually all counterfeit!

Each real coins weighs an "integral" number of grams (the weight can be expressed as an integer - a whole number) while the counterfeit coins weigh exactly one gram less than a real coin. 

You have a gram scale handy but you are only permitted to use it one time!

How do you determine with just a single weighing, not only which bag has the counterfeit coins, but the number of grams a coin weighs?