I’m grading a big backlog of homeworks today, so I don’t have time to do any really lengthy posts this morning. Thus, a poll question inspired by going through these homeworks:
While the class in question uses some quantum ideas, the poll is strictly classical, so no superpositions of multiple answers are allowed.
(Honestly, at some point, I would expect laziness alone to compel people to round their answers off before their hands cramp up from copying all these digits…)
As a mathematics student I much prefer when I can give answers exactly, rather than as approximations. When that’s not possible, then it depends a lot on the particular problem. I usually go with the lowest number of figures among those given in the statement.
I actually take a special glee in pointing out engineering estimates carried out to five or six significant digits in presentations.
“You have listed there your power output as 18.194 dBm, plus or minus 2. I think it’s actually 18.197 dBm.”
While I voted “It depends on the number of figures used”, that’s misleading. I generally assume that there’s been some rounding, so I tend to report one fewer digit than a correct calculation would show. Unless I know I’m not supposed to round off. And sometimes the statement of the problem tells me how many significant figures to report.
Having worked very hard for years to calibrate a major instrument to one percent accuracy (absolute), I don’t think I’ll ever report more than two significant figures again (at least if the measurement involves the sensitivity of an instrument).
I just consult NIST Technical Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results!
Kidding aside, I usually don’t care so much on homeworks unless there is an especially egregious number of digits, but I have a hard time suppressing my irritation when my graduate students insist on carrying out calculations to excessive sig. figs. when
1) There’s a huge error (due to things like the subtraction of two similar, noisy numbers).
or
2) They’ve screwed up the units, giving an answer with a ridiculous order of magnitude.
I’m just a technical writer (not trained as a scientist or engineer), but I was once asked to proof a solver verification manual (i.e., how close does the solver come to experimentally derived results for standard test cases). The thing had already been through several sets of reviewers (engineers and computer scientists) when it got to me. The whole book was like, “The peak stress in a simply supported beam of XXX mm length undergoing a distributed pressure load of X.XE6 N in -Z. Benchmark: X.XXE3 mPa. Solver: X.XXXXXXXXE3 mPa.”
And I’m like, “Guys, I know you all think of me as a glorified typist, but we have a problem here.”
I’m not paid to be popular.
One significant figure! (As a theorist, I habitually round off pi to 3.)
Way back when I was in College the answer was 2 to 3 since we used an ancient instrument called a slide rule to do calculations. Since we used 10 inch rules the answer is 2 to 3 depending on the first digit of the number in question.
In a few cases we used 6 place log tables which does teach one to be good at adding and subtracting (mostly in Chemistry)That was quite an experience. The slide rule does teach much better that the silicon mind of the calculator/computer which generates what was called back then empty precision.
You are missing an important option: The number of digits required by the policy set for that course.
Interesting poll results. How many of that vast majority will give a 1 sig fig answer when the value “10” or “500” is specified in the problem, or if an approximate value like 3×10^8 is used in the calculation?
But here is a question for a future poll, Chad:
What percentage of the problem’s points do you take off for an answer that has the incorrect number of sig figs? What if it has a bad digit for the number of sig figs used?