John Denker argues that it is insane to use significant figures.

Instead one should follow these guidelines:

• Keep all the original data. Do not round off the original data.
• In the introductory class, the following “house rules” apply:
  • Basic 3-digit rule: For a number in scientific notation, the rule is simple: For present purposes, you are allowed to round it off to three digits (i.e. two decimal places). Example: 1.23456×108 may be rounded to 1.23×108
  • For a number not in scientific notation, the rule is almost as simple: convert to scientific notation, then apply the aforementioned 3-digit rule. (Afterwards, you can convert back, or not, as you wish.)
  • The point of these rules is to limit the amount of roundoff error. As a corollary, you are allowed to keep more than three digits if you wish, for any reason, or for no reason at all. This is makes sense because it introduces even less roundoff error.
  • As another corollary, trailing zeros may always be rounded off, since that introduces no roundoff error at all. Example: 1.80 may be rounded to 1.8, since that means the same thing. Conversely 1.8 can be represented as 1.80, 1.800, 1.8000000, et cetera.
  • These rules apply to intermediate steps as well as to final results.
  • These “house rules” apply unless/until you hear otherwise. They tell you what is considered significant at the moment. As such, they have zero portability outside the introductory class, and even within this class we will encounter some exceptions. Still, for now three digits is enough. There is method to this madness, but now is not the time to worry about it. We have more important things to worry about.