Please read through this guide for reporting final results with appropriate significant figures. You should refer back to these guidelines and follow them throughout this course.
These guidelines apply only to final reported results. When reporting and working with intermediate results please do not round your results.
Something to consider when communicating your results is the number of significant figures (decimal places) you report. Imagine you calculated the mean value for the distance from the table and its uncertainty. The value you obtain from Google Sheets is 14.14030407 ± 0.40372678, and remember that we reported the number of centimeters (cm). So you should communicate this value when you write up your experimental results, right? Hold on: do you really know the value of d to the 8th decimal place? Our uncertainty of \(\delta d =\)0.40372678 cm tells us that we are unsure of the 1st decimal place, so we are definitely not sure about the value in the 8th decimal place of \(d =\)14.14030407 cm! This digit is insignificant; you don’t truly have that kind of precision in this experiment and cannot quote results that would imply otherwise.
This is where the term significant figures, or “sig figs” for short, comes into play. We only want to report digits that are significant — accurately reflect the precision of our experiment — in our results.
Here are the two steps to follow to determine significant digits:
Round and keep only one digit in your uncertainty.
Once you have determined the number of sig figs in your uncertainty, now round your measured value so the placement of the least significant digit matches that of the rounded uncertainty. Wow, that sounds confusing so let’s see how this applies to our example above: