Why are Significant Figures Important?

To see all my Chemistry videos, check out http://socratic.org/chemistry What's the point of significant figures?!? Really, significant figures (or significant digits) can be such a pain in the neck. What is the point? Significant figures tell us how to round, but they also make sure that the answer we get from a math problem is not more precise than the numbers that we started with. Accuracy and precision are both important with significant figures and digits.