How to deal with consequential rounding errors when verifying the works of others? to give a stupid example of a rounding error: on a test, the student is asked to calculate the circumference of a circle with radius 6.2. You personally did the math with π rounded to 3.14 and calculated 38.936, but one of your students rounded to 3.14159, and because of that their result is 38.955716.

Now, I doubt any decent teacher would discard this result as wrong, since the math itself was correct. However, what if this calculation was part of a much larger series of calculations for an academic paper, and the resulting rounding error throws off the entire result? It's easy to just come out and say "if you round X to 15 places instead of 14, your formula makes the English channel 10 meters wider" or "you rounded to 5 places, but if you round Y to 6 places, your result is no longer statistically significant", but it just seems like such a cheap way to give feedback for academics. Another example: "by rounding X to Y+1 places (or Y-1 places) in our formula to determine whether an event happened, we managed to shift 90% of our test group from 'happens 25% of the attempts' to 'happens 75% of the attempts'". It's an extreme example, but something like that

I know that such a remark can be seen as a meaningful one since it's a viable concern, but it's still quite a nitpick, and there's probably a reason why X was rounded to 14 places. Still, I can't help but think that a formula should work regardless of how many places you round X to.

If an academic paper you are reviewing could change result or even be invalidated due to rounding differently, how should that be handled in a peer review?
Now, I doubt any decent teacher would discard this result as wrong


I'm generally considered a decent teacher, and, yes, I'd consider that result partly wrong and I'd remove a mark or two, because students, especially from certain fields (e.g. engineering), should learn to get the values right, also, not only the math.

There are mathematical tools that allow to evaluate the effect of rounding errors and to deal with uncertainty of parameters in general: if in an academic paper, the authors overlooked the effect of the rounding errors (getting the wrong result or suggesting a model excessively sensitive to the parameters), I'd suggest to reject the paper asking for major revisions, pointing out at the proper literature.