Should Uncertainty Dictate Significant Figures in Physics Calculations?

[jgens]

My physics teacher said that our resultant answer should have the same number of sig. figs. as our uncertainty (he allows 2 sig. figs. at most); however, having done some of the problems, I get answers - when not rounded - such as 24.0 +- 0.1m, which when rounded to 1 sig. fig. results in 20 +- 0.1m which is not even near the minimum possible value. Did he perhaps mean to say the same number of decimal places?

Thanks!

 

[dlgoff]

Did he perhaps mean to say the same number of decimal places?

Check out this http://en.wikipedia.org/wiki/Significant_figures"

 

[jgens]

Having read the wikipedia page, I still don't think I have an answer. 24.0 has three sig. figs. while 0.1 has only one; therefore, if I round to 1 sig. fig. like my teacher said - result should have as many sig. figs. as uncertainty - I would get 20 +- 0.1. Is this correct?

 

[jtbell]

The simplified rule of thumb for uncertainties is:

When you add or subtract, round the final result to the least number of decimal places.

When you multiply or divide, round the final result to the least number of significant figures.

 

[cesiumfrog]

My physics teacher said that our resultant answer should have the same number of sig. figs. as our uncertainty (he allows 2 sig. figs. at most); however, having done some of the problems, I get answers - when not rounded - such as 24.0 +- 0.1m, which when rounded to 1 sig. fig. results in 20 +- 0.1m which is not even near the minimum possible value. Did he perhaps mean to say the same number of decimal places?

You're correct. If your experiment has uncertainty of tens of centimetres, then report your result to tens of centimetres.