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?
 A: 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.
A: Keep precision all the way through to the number you report and then truncate accordingly at the end. 
A: I have been taught and continue to teach that you should record (and use) the answers to your intermediate calculations (and/or conversions) with one extra significant digit beyond the number of significant digits that will be in your final answer.
A: https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Map%3A_Introductory_Chemistry_(Tro)/02%3A_Measurement_and_Problem_Solving/2.04%3A_Significant_Figures_in_Calculations
Just revisited this in chemistry this year. You actually have to apply the correct number of significant figures based on the rules of operations (addition/subtraction or multiplication/division) as you perform each calculation in a problem with multiple calculations. The purpose of using significant figures is not to get accurate results or results closest to what a calculator would get. The point of using significant figures is not to mislead the reader or person following your work in thinking that you used exact numbers when in fact you did not. So the more steps you have in a problem, the further your answer will be from the answer a calculator would derive. If you apply the correct number of significant figures in every step, you are accurately accounting for what you actually MEASURED (this is why they are applied to measured numbers, not exact numbers). And if you’re sitting somewhere computing the problem, you did not measure anything. We also do not just chose to use an extra significant figure or two but have to stick to the rules of operation. ie- least amount of significant figures for multiplication and division and lowest decimal place for addition and subtraction.
Hope the link above with consistent explanations and videos helps.
