General Rules to Help with Sig Figs

[alex_4l]

I have a few general rules that help me with counting significant figures, I can give more detailed ones for subtracting, adding, multiplying, etc if anyone needs them.

1) all non zero digits are significant ---example) 52931 has 5 significant figures, as does 17.333
2) interior zeros (ones that are sandwiches between numbers) are significant ---example) 101379 has 6 sig figs, 17.01 has 4 sig figs, 1.000001 has 7 sig figs
3) at the end of a number, trailing zeros (to the right of a non-zero number that fall after the decimal point are significant) ---example) 45.000 has 5 significant figures
4) trailing zeros that fall before a decimal point are significant ---example) 760. has 3 significant figures
5) trailing zeros at the end of a number, but before an implied decimal point are ambiguous/should be avoided ---example) 761. decimal doesn't matter, 760. explicit so the zero counts or 7.60 x 10^2
6) leading zeros (before regular numbers) (to the left or 1st non zero number) are NOT significant, they only serve to locate the decimal point ---example) 0.00031020 the zero before the decimal point doesn't count, neither does the one after the 2 at the end

hope that helps anyone struggling with significant figures!

[Matthew ILG 1L]

This is super helpful. Especially the one about the leading zeros and the decimal at the end of a number. I will for sure be coming back to this throughout the year. Thank you very much!!

[KayleyW_3L]

Can you explain how in #1, 5293 has 5 significant figures? I'm confused since I think it should be 4, but I might be missing something.
Otherwise, these tips are very helpful and thank you for sharing them.

[Qiu Ya Wu 4I]

Can you explain the difference between #4 and #5? Also, would the two zeroes before 341 but after the decimal point in 0.00341be considered insignificant?

[Joanne Kang 3I]

0.00431 would be considered 3 sig figs, meaning the three zeros in front are insignificant.
For 4 and 5
ex. 50.00 and 5.000 x 10 has 4 sig figs
0.00501 and 5.01x10^2 has 3 sig figs

[Anvi Brahmbhatt 4A]

Thank you so much for listing out the rules! It is very helpful to refer to, especially when working out problems. I also think for #1: 5293 has 4 significant figures.

[Patricia Chan 1C]

Thanks so much for the refresher on sig fig rules! In number one, however, I think 5293 has four sig figs instead of five. Nonetheless, thanks again!

[Ryan 1K]

I understand how to keep track of sig figs after calculations, but I'm not sure when I should use them. Do I round between each calculation or at the very end for the final answer? If at the very end, how do we know how many sig figs to use?

[andrewcj 2C]

I really think 5293 has 4 sig figs, not 5. I think if it was 5293.0, it would have 5 sig figs.

[Ian Morris 3C]

I am confused as to when to apply sig figs. Should I apply them throughout my problem at each step, or just at the end?

[Anisha Chandra 1K]

I think you would apply them at the end to avoid round-off error.

[Kyle Thorin]

Generally, chemistry problems will require you to round at least to the hundredth. The more precise your answer is, generally the more significant figures you'll want in your answer. When doing calculations, it is common to at least round to the hundredth.

[Emma Popescu 1L]

Will we be penalized if we use more significant figures than needed?

[Rishika Yadav 3D]

My T.A. said that we don't need to worry about sig figs too much, and that we should focus more on always having units.

[alex_4l]

@KayleyW_3L
That was a typo on my end! it should be 4 significant figures for number 1, sorry for the confusion :)

[alex_4l]

Will we be penalized if we use more significant figures than needed?

You might be penalized in a lab since it is more important with the measurements, I'm not sure what our professor deems to be okay with for significant figures and how strict it is, but when solving a problem you want your answer to match the number with the least amount of significant figures. Even if it isn't too important with significant figures, it is beneficial to try and practice it since it might be more serious in other advanced chemistry classes. Hope that helps!

[alex_4l]

I am confused as to when to apply sig figs. Should I apply them throughout my problem at each step, or just at the end?

You apply them at the end with your final answer, don't worry about doing it throughout the problem. In lab with measurements, the last digit is always the estimated one in order to accommodate for human error

[Jasmine Fendi 1D]

Thank you! This was very helpful. When I am doing a problem, I would keep as many digits as possible and round off at the end. At the end of a problem, how do you know how many sig figs to use? In high school I used how every many there were in the given values in the problem.

[alex_4l]

Also, if you end with an answer of let's say-- .00056 and you want to put it in scientific notation, you would want to put that answer in the amount of significant figures of the number in the equation with the least amount of sig figs.
So for example:
(7.45 x 3) divided by (5.7 x 10^6)
7.45 has three SF, 3 has one, and 5.7 has 2 --- therefore, you would want your answer to have 1 significant figure since the number 3 has the least
in the calculator the answer would be 3.921052632 x 10^-6 but would in turn be rounded to 4 x 10^-6

Usually in a problem the question will specifically ask to have the answer in the correct number of significant figures but if it isn't stated it's always good practice to do it anyways in order to get the hang of it