# Calculating Uncertainty in multiplication/division (Volume&Ration)

by nut.the.dutch
Tags: uncertainty, volumeandration
HW Helper
P: 5,341
 Quote by nut.the.dutch 2. Find the uncertainty in the volume of a cookie. > Express your answer using one significant figure. 4. Find the uncertainty of the ratio. > Express your answer using one significant figure. uncertainity = sqrt [(uncertainty of A/A)^2 + (uncertainty of B/B)^2] I plugged in: sqrt [(.02/8.5)^2 + (.005/.07)^2] = .07146... = 7*10^-2 (one sig fig) ...and it was wrong.
Welcome to PF.

The formula from the Dartmouth site which uses the RSS of the relative errors should be OK. To apply it properly you need to account for the area uncertainty as the square of the dimension that you would have used. If you would have calculated the area as πd²/4, then you would want to add d's contribution to uncertainty twice.

Hence ((Δd/d)² + (Δd/d)² + (Δh/h)²)1/2
 HW Helper P: 5,341 On the other hand your course may also be treating uncertainty in a more conservative manner and the multiplication rule your teacher is using may only be based on the simple sum of the relative uncertainties. In which case you may be expected to use (Δd/d) + (Δd/d) + (Δh/h)
 HW Helper P: 5,341 This was why I suggested you use the πd²/4 for area, as it should clarify how you would take the relative uncertainty. (Δd/d)² ---> (.002/8.5)² Yes. Add it twice. Note your error ±.002 over 8.5 cm as per the original statement
 HW Helper P: 5,341 RSS = Root Sum of the Squares
P: 7
 Quote by LowlyPion This was why I suggested you use the πd²/4 for area, as it should clarify how you would take the relative uncertainty. (Δd/d)² ---> (.002/8.5)² Yes. Add it twice. Note your error ±.002 over 8.5 cm as per the original statement
Alright. I don't think I see what you're saying, to me it looks like you're just repeating to do what I've already done, which is:

 If I use the diameter, and not the radius: = sqrt[(.02/8.5)² + (.02/8.5)² + (.005/.07)²] =.0715060381 > again, works out to the same number
.

Are we speaking past each other? Becuase as I said, the .07....number I keep coming up with is incorrect. MasteringPhysics automatically checks answers, it's deemed that one wrong...
HW Helper
P: 5,341
 Quote by nut.the.dutch Alright. I don't think I see what you're saying, ...... If I use the diameter, and not the radius: = sqrt[(.02/8.5)² + (.02/8.5)² + (.005/.07)²] =.0715060381 > again, works out to the same number ...
Let me say it again:

Note your error ±.002 over 8.5 cm as per the original statement
 P: 7 Aagh - I'm so sorry, I copied the original problem wrong, it's not .002, but .02cm (and still .005cm for the other). Sorry for the confusion. :/
 HW Helper P: 5,341 Ok. That's fine. Then are you sure your instructor is expecting you to take the RSS to determine uncertainty propagation? Because regardless, the error of the diameter is so much smaller than the error of the thickness, that the RSS will be dominated by the thickness error. Might it simply be the sum of the relative errors in your course for taking multiplication/division uncertainties? In which case that sums to .076. But remember what you get from either method is a relative uncertainty result that would be expressed as a %. If they want the error expressed as an absolute volume then you still need to multiply that % by the nominal calculation.
 P: 7 No, I have no idea what he expects. Of the entire problem set for the section, this is the only problem with uncertainties. This is the first homework set though, but/and it's 'physics for engineering majors'. We haven't covered before, so maybe you're right and he's looking for a simpler solution. What you're saying, is that I take the 7*10^-2, and multiply it by the nominal calculation, so .076*4.0(volume) and .076*120(ratio). YEEEEEEEEESSSSSSS!!!!!! Thank you! That works, and I also get it.
 HW Helper P: 5,341 If the .076 is correct then the instructor is not using the RSS, he is using the simple sum of the relative errors as his multiplication/division rule, with the relative error of the diameter taken twice because of its effect on area. Good luck.
 P: 7 Yeah, .076 multiplied by the actual result (ratio, volume) was right. Thanks again!

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