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nut.the.dutch

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**[SOLVED]Calculating Uncertainty in multiplication/division (Volume&Ration)**

Hello all.

## Homework Statement

As you eat your way through a bag of chocolate chip cookies, you observe that each cookie is a circular disk with a diameter of 8.50 +/- .002cm and a thickness of (7.0×10^−2) +/-0.005.

1. Find the average volume of a cookie. > Express your answer using two significant figures

2. Find the uncertainty in the volume of a cookie. > Express your answer using one significant figure.

3. Find the ratio of the diameter to the thickness. > Express your answer using two significant figures.

4. Find the uncertainty of the ratio. > Express your answer using one significant figure.

## Homework Equations

I already got the average volume and ratio, but I'm having a hard time solving for the uncertainty. BTW, this is a MasteringPhysics problem, so it's online and we get feedback, but every incorrect attempt lowers your possible points.

1. Volume:

V=A*thickness = (pi*4.25^2)*.07 = 3.972...cm^3 = 4.0cm^3 (2 sig. figs)

3. Ratio = diameter/thickness = 8.50/.07 = 121.4285714 = 120 (2 sig figs)

## The Attempt at a Solution

I read the physics textbook, but I'm still confused. It talks of implicit uncertainty (sig. figs). The example it gives is:

"We give the thickness of the cover of this book as 2.91mm, which has 3 sig.figs. By this we mean that the first two digits are known to be correct, while the third digit is uncertain. The last digit is in the hundredths place, so the uncertainty is about .01mm"

So I tried using the volume (4.0 cm) - it has 2 sig. figs. According to the book, the last digit is the 0, and it's in the tenths place, so the uncertainty would be = 0cm?! That's obviously wrong. Same thing when you try to repeat the process for the ratio (120) - there are two sig figs, the first digit is known to be correct, and the second is uncertain 2 is in the tens spot, so the uncertainty would have to be 20 - which again is wrong - I plugged it in and it was wrong.

I was trying to find help online, and I came to this site: http://www.dartmouth.edu/~chemlab/info/resources/uncertain.html"

If you scroll down, it comes to uncertainty in multiplication or division, and they give you the equation:

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.

Essentially, I'm stuck and not sure how exactly you *find* uncertainty. I read a lot of the uncertainity posts on here, but it still hasn't helped, https://www.physicsforums.com/showthread.php?t=213084&highlight=uncertainty"reccomends the same formula as the dartmouth site, and I still get that the answer is wrong.

I wish I could show more work, but all of my work is wrong, and after that, I was just trying to guess using random combinations of the given uncertainties (.02cm and .005cm), and I doubt it'd be much use. Other than going into ask the professor himself, I've exhausted all the other options, none of what I read online or in the textbook clicked to show me how to go about answering the problem.

Thank you very much for any help!

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