what to do with s.f. and rounding in a series of calculations

[Zellmer, Robert]

I believe I mentioned this in lecture, but I've received a few questions about it after

lecture this week and in e-mails over the last couple of days.



When doing a series of calculations, you should keep track of the s.f. in each step but

carry extra digits to the next step.  How many extra?  At least one.  I usually store the

number with lots of extra digits (in my calculator's memory registers - which you all

know how to use after having your romantic evening with your calculator).  In lecture I

often carry several extra digits and underline the last significant digit.  You've seen me

do this if you've been in lecture.



On a quiz, you should carry extra digits and round the final answer.  Doing this

prevents what we call "round-off" error in the final answer.



For lab, in the sample calculations you determine a number for a step, including extra

digits.  Then write it with the correct number of s.f. (and units of course).  If the number

is required in the report or report quiz (presentation of data section, table, etc. ) you

record it there with the correct s.f.  If you need to use the number in a subsequent

calculation you should use the un-rounded number (with the extra digits).



Hopefully, this makes sense.



Dr. Zellmer
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