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Please help me with significant figures (general chemistry concept, not homework)
Regina Fong
Allons-y, AlonsoRegistered User regular
Allons-y, AlonsoRegistered User regular
I'm a junior minoring in chemistry. Somehow, against all odds, despite being objectively horrible at mathematics, I actually do well in chemistry. I think this is the reason that I can't convince my instructor to explain sig figs to me like I am a dim-witted child.
Seriously.
Explain this to me like I am a dim-witted child. The wikipedia article makes my eyes bleed. I can't seem to parse my textbook's explanation. It's possible that I am too stupid to ever grasp this (apparently simple) concept, but lets try anyway.
I get that if I have, say, 0.15 mL of something and 0.222 mL of something else (lets say one of the flasks was less precise and we were lazy) and I combine them, I do not have 0.342 mL of liquid. I get that. I have 0.34 mL because of sig figs.
That part I get.
The part that I don't get, and every time I try to understand it I feel like I am having a brain aneurysm is if I have (using an example from an old lab that's already been graded so you're not helping me cheat) 14.290 grams (a watch glass with product on it) and the original weight of the glass was 13.702 g what do I have?
14.290-13.702 = 0.588 g
In real math. But there are five significant figures in both of the above weights, so shouldn't the answer be 0.58800 g? To also be five significant figures?
Except that can't be right, because the scale only measures out to 0.000, adding two zeroes to the end of it is like magically creating additional accuracy for the scale that isn't there.
This is the precise spot where significant figures breaks my brain and I give up and just write (for example) 0.588 g and lose a point on the lab. And it's only 1 point, it's not like we're talking life or death here.
But if it's at all possible for me to understand this concept, I would like to understand it. Thanks.
Seriously.
Explain this to me like I am a dim-witted child. The wikipedia article makes my eyes bleed. I can't seem to parse my textbook's explanation. It's possible that I am too stupid to ever grasp this (apparently simple) concept, but lets try anyway.
I get that if I have, say, 0.15 mL of something and 0.222 mL of something else (lets say one of the flasks was less precise and we were lazy) and I combine them, I do not have 0.342 mL of liquid. I get that. I have 0.34 mL because of sig figs.
That part I get.
The part that I don't get, and every time I try to understand it I feel like I am having a brain aneurysm is if I have (using an example from an old lab that's already been graded so you're not helping me cheat) 14.290 grams (a watch glass with product on it) and the original weight of the glass was 13.702 g what do I have?
14.290-13.702 = 0.588 g
In real math. But there are five significant figures in both of the above weights, so shouldn't the answer be 0.58800 g? To also be five significant figures?
Except that can't be right, because the scale only measures out to 0.000, adding two zeroes to the end of it is like magically creating additional accuracy for the scale that isn't there.
This is the precise spot where significant figures breaks my brain and I give up and just write (for example) 0.588 g and lose a point on the lab. And it's only 1 point, it's not like we're talking life or death here.
But if it's at all possible for me to understand this concept, I would like to understand it. Thanks.
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By that rule, your answer should be correct, since 14.290 and 13.702 both have 3 decimal places, your answer of 0.588 should be right, since that is to the third decimal place. Your lab says 0.58800 is correct? Are you sure that the person who graded it graded it correctly?
Do you have additional examples? It really does look like you have it right.
Lets assume you are talking about grams.
14290 grams minus 13702 grams gives you 588 grams
There has been no measurement out to milligrams, centigrams or decigrams so you could not say you accurately measured 588000 milligrams, 58800 centigrams or 5880 decigrams.
Scientific notation would be the ideal notation:
5.88e^-1
or
5.88 x 10^-1
Thank you for parsing that for me, I feel like I can take that explanation to my instructor and ask her yay or nay and get an answer that I can go forth with.
I actually don't have any more examples. I'm in organic chemistry now, and there's very little stoichiometric calculation at all. It's almost math-free. So this isn't something that's beating me up in the class, I have an A and am doing quite well at... drawing weird stick figures and spilling chemicals, which seems to comprise the bulk of organic chemistry.
And my lab didn't say that was correct, I had 0.588 and there was a red mark next to it, and the instructor made a general comment to the class about our significant figures being terrible and how we should know better from general chemistry. Maybe the red mark didn't actually mean there was a point deduction. I got 58/60 on the lab. Mostly because I am good at spilling chemicals in the right places, I think.
That makes sense to me, and it's why I asked about that particular calculation. It makes no sense whatsoever to go from xx.xxx to .xxxxx to me at all. So, I guess, good. My sense of logic lives to fight another day.
I haven't seen anything in scientific notation since gen chem. O-chem seems to be all about visuals. Thanks for the response!
In that case I think you're on the right track, as far as sig figs are concerned.
You probably lost points on your laugh. From what I gather, whether it's university or even community college chemistry I'm pretty sure they grade your maniacal laughter really harshly. Schools want to make sure they put out high quality grads, of course.
For addition and subtraction, just write them down, aligning the decimal point. Fill in the blank spaces with a ? mark, so they all reach the same decimal place. When you add all the numbers together, you cannot be certain what any of the ? numbers are, right? That's the idea behind sig figs.
So you once you have summed up all the values, round the number to the decimal place column with no ? marks.
but yeah your calculations seem right so i dunno.
This is the lowest level explanation of sig figs I've ever heard, and that's a good thing, very good. Thank you.
For example, if your digital balance has an uncertainty of +/- 0.02 g, then you'd write any measurement with only two decimals. If you do any calculations, you simply use error propagation rules (which can be found anywhere online).
Nintendo Network ID: PhysiMarc
Pertinent link: https://www.khanacademy.org/math/arithmetic/decimals/significant_figures_tutorial/v/significant-figures
I've never seen anything like that with equipment in a chemistry lab. If a scale measures out to 2 decimals then that's what you use, if it's three, then three.
When measuring by eye in something like a traditional thermometer you're actually expected to estimate one increment beyond the numbering. So even though the thermometer gives you a temp like 100 degrees, you're supposed to eyeball 100.X and use that.
I won't have to deal with that then. After organic x2 I have biochem and then I'm done with my minor.
Significant figure indicates that the number has value. .588001 would be significant, .588 is semantically and mathematically the same as .58800.
This concept seems... off.
I guess that explains why students complain that physics labs are useless: they don't actually get to apply what we're teaching them in their other labs (until a few years down the road, I assume).
Nintendo Network ID: PhysiMarc