# When do I apply Significant figures in physics calculations?

I'm a little confused as to when to use significant figures for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of $500~\mathrm{m}$ in $50~\mathrm{s}$.

Would I need to apply the rules of significant figures to this step of the problem? $$C = 2\pi (1000~\mathrm{m}) = 6283.19$$

Or do I just need to apply significant figures at this step? $$\text{Average speed} = \frac{6283.19~\mathrm{m}}{50~\mathrm{s}} = 125.664~\mathrm{m}/\mathrm{s}$$

Should I round $125.664~\mathrm{m}/\mathrm{s}$ to $130~\mathrm{m}/\mathrm{s}$ since the number with the least amount of significant figures is two?

-
mathematical-physics probably isn't the right tag for this. But I don't know what is, mathematics isn't appropriate either. – tpg2114 Feb 2 at 0:23
@tpg2114 I agree, I couldn't find an appropriate tag for this question. – Scotty Feb 2 at 0:25

## 2 Answers

You should always find an answer that is a formula, and then only apply significant figures once you get to the one final step of substituting your numbers back into the problem in place of variables.

Avoid multiple intermediate steps of substituting numbers at all costs. Not only will this save your pencil a lot of work, but it will also cause your answer to be more accurate, as rounding errors can pile up, even when using a calculator.

-
 So the correct answer would just be 130 m/s then, right? – Scotty Feb 2 at 0:23 @Scotty Yes, if the 500 and 50 given to you each had at least 2 sig figs. Some conventions are "50" has one sig fig (so your answer should round to 100) and "50." (note the decimal) is more precise. You should check with your instructor/textbook for what the conventions are. – Chris White Feb 2 at 0:37

Keep precision all the way through to the number you report and then truncate accordingly at the end.

-