johnny309,
If I remember my math, the number of significant figures in your answer cannot exceed the lowest number of significant figures in any of the factors used to obtain that answer. For example, you said
16.387064 cubic centimeters x 19.32 grams = 316.59807648 grams
Since 19.32 has only 4 significant figures, the best answer would be 316.6, which also has 4 significant figures. The other numbers in your answer are meaningless. Think about it. 19.32 may actually be something like 19.317849032, rounded off to 19.32. Or, it might be something like 19.3217639004, rounded off. Both will give different answers in the above equation, but both will round off to 316.6, at best.
No offense intended. I just see this sort of thing done all the time and, since I'm so anal about these things, it drives me nuts. Common 8 or 12 place calculators are definitely the blame for this heresy. In the ancient years, before hand-held calculators (about 1974), those of us who had to use logarithm charts or log log slide rules to make these calculations understood this important premise much better. BTW, I hope we are still friends. :lol:
http://en.wikipedia.org/wiki/Significant_figures
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch1/sigfigs.html