I thought you were talking about using the weight of the penny to estimate the amount of money in a full gallon jar (err, wait, that is what you're talking about!). I thought you were just over thinking it! (err, wait, I still think that!) The thing is, as others have pointed out, the way in which the pennies are arranged, or in this case, just happen to fall, in the jar is going to be a factor in how many pennies will fit in the gallon. It sounds, to me, that you're planning on melting the pennies down and then filling the gallon jar with the molten pennies, all the while, taking note of how many pennies worth of molten metal you've poured. As I type this, I'm even more convinced that you're over thinking the problem. The main thing to agree on, though, is that the pennies will never fall into the jar in exactly the same pattern, and sometimes, more pennies will with than at other times, just because of the randomness of their falling. A good scale will get you the right number every time, though there may slight differences due to the amount of dirt on each penny.