In class, my teacher mentioned that you should complete a calculation without considering significant figures and then at the very end, round to the proper number of significant figures. Why couldn't we just round the numbers after each step of the calculation? Is there a difference?
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The notion is that "excessive" rounding in the intermediate calculations results in a rounding error in the final result. Consider $$1.01^{5}\times 6.7 = 7.0$$ but if you round 1.01 to 1 at each multiplication step then $$1.0\times1.0\times1.0\times1.0\times1.0\times6.7 = 6.7$$ – MaxW Sep 12 '18 at 05:16
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No rounding during calculation is a bit impractical, but you should always keep one additional digit in the numbers until properly rounding the final result. – Karl Sep 12 '18 at 06:49
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@Karl - I'd carry two extra digits. That doesn't seem to be much of a burden for calculations done with a modern calculator. I couldn't do that though when I was working out problems with a Post Versalog slide rule which I used from high school through first year of graduate school. – MaxW Sep 12 '18 at 07:16
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@MaxW Or do the obligatory error estimation. ;-) – Karl Sep 12 '18 at 17:02