We had 45 responses to yesterday’s poll/quiz question– thank you to all who participated. The breakdown of answers was, by a quick count:
How do you report your answer in a lab report?
- 0 votes A) 4.371928645 +/- 0.0316479825 m/s
- 3 votes B) 4.372 +/- 0.03165 m/s
- 18 votes C) 4.372 +/- 0.032 m/s
- 21 votes D) 4.37 +/- 0.03 m/s
- 2 votes E) Some other answer that I will explain in comments.
So, it’s a narrow victory for D, among ScienceBlogs readers.
The correct answer and the reason for the poll are below the fold.
As far as I’m concerned, the correct answer is D). There’s absolutely no reason to report digits of the answer past the first digit of the uncertainty, because 0.002 is much smaller than 0.03. Even if you report that next digit, it’s way smaller than the error associated with the measurement, and serves only to give a false impression of precision.
C) is close, but I think that the proper procedure is to round the uncertainty to one significant figure, and round the reported value to the same number of decimal places as the first digit of the uncertainty. This is what we have agreed upon as a department, and this is the procedure that is spelled out in our lab writing guides.
(Someone in comments mentioned the “rule of 19,” which is that you keep two digits of uncertainty when the first is a 1. I’m pretty much ok with that, though I’d still round down to one digit for anything less than 15.)
The reason for the question is that I’ve been grading labs recently, and my students almost universally choose the equivalent of B) (those that don’t go for A), at least. I get ridiculous numbers of uncertain digits reported, all the time. And even when I take ten minutes of class time to go over the rules, they stick with A) or B). Even when they’ve hand multiple lab classes explaining this procedure, they mostly stick with B), and I’ve had senior physics majors give me lab reports taking option A), which is just mind-blowing.
For some reason totally beyond my comprehension, “Round the uncertainty to one significant figure, and the reported value to the same number of decimal places” just baffles my students, year in and year out. I can’t for the life of me understand why– it seems like common sense to me– so I thought I’d try polling people on the Internet to see if there’s some sort of deep-set attachment to B) that I just don’t share. Maybe there’s some evolutionary advantage conferred on savannah-dwellers who like lots of digits in their math, and I’m the result of a late-arriving mutation (get me Steven Pinker, stat!)…
It turns out, though, that you all are mutants, too, so that’s out. But if anybody out there can shed any light on this difficulty, or suggest some way to teach this that will actually be effective (docking points isn’t enough– believe me, I’ve tried), I’m at the end of my rope, here.
If you answered D)– or even C), I’d take C)– how did you learn that rule? And what would you suggest for helping students break out of B)?