7 replies to this topic

[Trololol Marf]

If I have an uncertainty that does not fall within the range of the last digit of my measured value, do I just neglect it?

Example: 0.12345+/-0.0000000023

Assume that the uncertainty is calculated; it's not an uncertainty of reading error.

[El Che]

I'm not so sure, but what you think is right in my opinion. I mean, it wouldn't make any difference with regards to your result, would it? However, I believe it's a good idea to show it on the paper, though.

[Procrastination]

Okay so first of all, you do realize your example is not correct? uncertainties should not be quoted to two significant figures, they should only have one number basically. Taking into consideration this, you should write it like: 0.00blahblah002 and not 0.00blahblah0023. Okay now, it is actually perfectly fine to have uncertainties like that, calculations shouldn't be affected and it doesn't make any difference with regards to your result. This kind of uncertainties just state that the correct value of a measurement is within the range of: (adding the uncertainty to the recorded value, the recorded value minus the uncertainty). In the other hand, you should be careful, you must not write 0.12345+/-0.0000000023. Remember the number of decimal places should be the same in both the uncertainty and the recorded value so you'd be likely to say: 0.123450000+/-0.000000002

That's pretty much it. Hope it helped

Edited by Procrastination, Jan 03, 2012 - 16:59.

[Trololol Marf]

Procrastination, on Jan 03, 2012 - 16:51, said:

Okay so first of all, you do realize your example is not correct? uncertainties should not be quoted to two significant figures, they should only have one number basically. Taking into consideration this, you should write it like: 0.00blahblah002 and not 0.00blahblah0023. Okay now, it is actually perfectly fine to have uncertainties like that, calculations shouldn't be affected and it doesn't make any difference with regards to your result. This kind of uncertainties just state that the correct value of a measurement is within the range of: (adding the uncertainty to the recorded value, the recorded value minus the uncertainty). In the other hand, you should be careful, you must not write 0.12345+/-0.0000000023. Remember the number of decimal places should be the same in both the uncertainty and the recorded value so you'd be likely to say: 0.123450000+/-0.000000002

That's pretty much it. Hope it helped

Thank you. I have a few questions regarding what you said though.
So it's incorrect to ignore the uncertainty, but it's necessary to add the zeros for the decimal places?
Also, if the uncertainty should only be quoted to 1 significant figure, you mean that's if the uncertainty is under 0 right? (pretend I calculate an uncertainty of 7.54 ... it becomes 7.5?
And if you could tell me or source where you're getting this information from, that'd be awesome

Oh and and and! lol
If I have two calculated uncertainties, and I have to add them, how would I go about doing that?
e.g. 0.1+0.0000001

I heard that when doing calculations, we round to the least precise value; I'm wondering if it's the same for uncertainties...

Please help. I'll love you forever.

[Procrastination]

Oh oh oh, don't worry. I'm glad to help you.
Yes it is incorrect to ignore the uncertainty, except when it is not significant at all. Say your recorded value is 5248622 J and your uncertainty is 0.000000000000000000000000002 J. If you're doing an IB exam or stgh similar, you must state it, but it is not relevant so it is correct to neglect it. For example, when you're doing an IA sometimes you can't see any error bars in your plotted graphs so you just state the error range can be ignored since it is nothing compared to your recorded measurements. In the other hand final uncertainties should be quoted to one significant figure ALWAYS, it doesn't just applies when they're under zero. And your example is wrong, lol, don't worry. Say you have to state what's your final uncertainty with just 1 s.f and according to your calculations you got 7.54. You do not approximate to 7.5 and you can't indeed leave it like that. You must approximate to 8 (I don't remember if 7.5 is rounded up to 7 or 8 so let's pretend it is 8). The reason why you do this is because as I've stated before, you must quote your results to one s.f and 7.5 has two. 8 or 7 are just one, so this should be the final answear. My knowledge about this topic comes from the things I've been taught by my teacher and some course companions and study guides I have (Hamper and Kirk designed specifically for the IB diploma) so this time, you'll have to trust me lol.
Okay so let's continue: you don't always sum up two uncertainties, the operations you do with them depends on the type of calculation you're doing with your recorded values. I mean, when you're just adding or - two values with corresponding uncertainties, you just sum them up as it applies for your example: 0.1 + 0.00001 = 0.10001 (however, as you might have learned, you must approximate, hence the final uncertainty for your calculated result would be just 0.1 lol, I know, pretty dumb, the second uncertainty can be neglected this time). There are other situations when you sum up percentage uncertainties (when your recorded or given values are divided or multiplied) and there are other ones when your percentage uncertainties are halved (when the recorded values are given to a square root relationship). If you need to get the percentage uncertainties or get the absolute uncertainties from percentage ones just use a rule of three. Finally, while you're doing calculations, your final result should be rounded to the least precise value, however, this doesn't applies for the uncertainties. After all the calculations you just quote your result to one s.f. And that's it. Hope it helped

Procrastination

Edited by Procrastination, Jan 04, 2012 - 04:55.

[Trololol Marf]

Thanks a lot, my main concerns have been addressed. But I think the Pearson textbook speaks differently... where I've seen the absolute uncertainty given by two figures instead of one. I guess the rule can be a bit flexible? It'll also help out my calculations a lot to be more precise...

-I imagine the one s.d. rule is quite different for percentage uncertainties? I've seen rounding and a 7.4% uncertainty in the Pearson textbook.

[Drake Glau]

Pretty sure Procrastination discussed everything you need. If your uncertainty is that low I'm assuming you're in physics? Because if not you might want to check whatever it is that is giving you this uncertainty.

Uncertainties go by # of decimal places, not specifically the s.d.
0.03+/-0.22 is still correct. The precision of an instrument is based off how many decimals it can display. Of course absolute uncertainty is the uncertainty for electronic measurements so that might be the reason for why you saw that in the book.

For a graduated cylinder, for example, it will also be half the smallest measurement possible, or 0.5mL in this case. This is where you would only have that one s.d. because you really only need one

[Trololol Marf]

(o_0) I didn't know that neglectance isn't a word

It's a chemistry lab (absorbance experiment dealing with equilibrium concentrations); but I thought I'd make the thread in the experimental sciences because the rules for uncertainties apply for any lab in any science.

Quote

0.03+/-0.22 is still correct. The precision of an instrument is based off how many decimals it can display. Of course absolute uncertainty is the uncertainty for electronic measurements so that might be the reason for why you saw that in the book.

Sorry for so many questions, but your replies have made me wonder a bit more. Is it actually possible for a uncertainty to have two s.d.s in an electronic measurement? I thought it'd always be 0.1 or 0.05 (with only one) and it couldn't really be 0.10 or 0.050 (or something related to that) because the decimal places of the uncertainty is independent of the measured value (which has to correspond) ^ That's true, right?

Right now, I'm calculating absolute uncertainties by converting them from percentage ones.  But when I do the absolute uncertainty is way smaller that measured value, and the numbers keep going... do I just round to one significant digit, and make the measured value match the number of decimal places?

Thanks for all the help.