Engineers: A Paradox w/Sig Figs

[Napier]

1. I propose that Jinx is talking about some kind of “sig fig” that is wholly unrelated to significant figures. Maybe some kind of fruit, or a term borrowed from another language. Only then does the OP make sense.

2. The general rule I learned is to round up if the lost digits start with greater than 5, down if they start with 4 or below, and to make the last reported digit even if you’re losing exactly 5 and zeros off the end. This fixes a slight statistical bias in the above posted rounding method.

3. I vote for keeping all the digits it’s convenient to keep at least up to the final answer, because later you can often figure out where you got your values by inspecting the less important digits. If error estimates are important - that is, if someone’s paying attention to them - much better to make them explicit.

4. There are very wide ranges of how many significant figures people care about. I’ve estimated bending of beams using chords of circles, and worked with standardized time values (like fractional seconds since 1/1/1960), and calculated phase information for GPS signals, and solved problems in special relativity - all these required more than 12 significant figures.

[bostonpete]

@1010011010

If you’re not dealing with the real world limitations of real world measuring devices… sig figs are pretty much theoretical academic masturbation.

Hmmm. I would have said that any calculation that doesn’t have to account for the real limitations of measuring devices (and therefore require an understanding of sig figs) is theoretical academic masturbation…

[Napier]

>any calculation that doesn’t have to account for the real limitations of measuring devices (and therefore require an understanding of sig figs) is theoretical academic masturbation

This is going to bring a fun new feeling to balancing my checkbook!

[1010011010]

@Stranger On A Train

Generally when rounding figures you round up at 5 or greater and round down at less than 5. Actually, the upper bound should have been 2.5634999…, but for practical purposes you usually just look at the first digit past your significant figures and truncate.

I am unfamiliar with the conventional methods of rounding numbers. Thank you for explaining how it is done in your country. ¦¬)

5 is an ambiguous case.
2.563 + 0.0005 = 2.5635, not 2.5634999…

Also, 2.5625 is just as far from 2.563 as 2.5635… there is nothing that says one rounds to 2.563 and the other doesn’t besides convention. And there are several rounding conventions. If rounding down were the usual case, we’d be having this discussion about 2.5635 to 2.5625000…0001

@Napier

This is going to bring a fun new feeling to balancing my checkbook!

Many cash measuring devices can measure to the cent at an arbitrarily high level of precision. I.E. one cent is 1. x 10^-2 cents, in sigfig lingo. If you want to include the infinite number of trailing zeros (all significant), though, feel free.