Question

What is the approximate uncertainty in the area of a circle of radius 3.1×104cm?
Express your answer using one significant figure.
ΔA =

Answer 1

i got an area of 3.0×109cm2

Answer 2

@agent0smith

Answer 3

erm... i guess maybe we're just doing it based on the significant figures...?

(3.1×10^4)^2 = 9.61x10^9 cm^2 which we have to round to 9.6x10^9 cm^2

Which i guess makes the uncertainty the diff. between the exact and rounded answers
9.61x10^9 - 9.6x10^9 = 1x10^7 cm^2

not sure about this but it seems reasonable.

Answer 4

its says the answer is ΔA = 2×10^8 cm2
i gave up on this problem bc i couldnt even figure it out

Answer 5

Oh wait, i did it as a square lol...

Answer 6

If you use the correct area formula:
\[A=\pi r^2,\]but follow the same method as agent did, you'll get the correct answer.

Answer 7

i found the area but i dont understand the uncertainty part

Answer 8

Uncertainty is because you have to round for significant figs

pi*(3.1×10^4)^2 = 3.019x10^9 cm^2 rounded to 3.0x10^9

3.019x10^9 - 3.0x10^9 = 2x10^7 cm^2

Answer 9

You need the difference between the full unrounded answer and the answer which has been rounded to the correct number of significant figures — this represents the uncertainty in your final answer.

Answer 10

@agent0smith in the second step after you found area wouldnt that cancel out?

Answer 11

is there a formula for finding uncertainty?

Answer 12

No, because you're subtracting the rounded answer, from the unrounded answer. Remember that the original problem only gives 2 significant figures (3.1×10^4 is only two, the 3.1)

Answer 13

im confused, so we take 3.0 x 10^9 (area) and subtract it with 3.1 x 10^4 ?

Answer 14

No, we take 3.019x10^9 cm^2, round it to 2 significant figures, then subtract the rounded answer from the unrounded answer.

Answer 15

so 3.0 - 3.1 = 0.1 , i cant see what your actually doing can you please show the steps i have an exam on monday and really need help

Answer 16

Idk how else to show it.

Find the area, using pi*r^2, then round that area to 2 sig. figs

then subtract that rounded area from the unrounded area.

Answer 17

3.0 is in 2 sig figs then subtract that to the number that is not in sci notation

Answer 18

i got 0

Answer 19

i give up on this..thank you for helping me =D

Answer 20

Calculate the area using the value:\[r=3.1\times 10^4cm\]\[A=\pi r^2=\pi(3.1\times 10^4cm)^2=3019070540cm^2\]Now round that value to the correct number of significant figures:\[A_{rounded}=3.0\times 10^9cm^2\]Take the difference between the two values, NOT heeding significant figure rounding at first:\[Uncertainty=A-A_{rounded}=3019070540cm^2-3.0 \times 10^9cm^2=19070540.1cm^2\]And since the question asks for the uncertainty with 1 significant figure:\[Uncertainty = 2\times 10^7cm^2\]

Answer 21

it says it to the 8th power though thank you for clearing some of that out

Answer 22

I think this method of determining uncertainty is a bit non-kosher. Error analysis is a weak area of mine, so your best bet is to wait for someone else to come around or to ask your professor to expand.

Answer 23

alright thank you so much for your help =D

Answer 24

Ah, I've figured out the issue. I was thinking it was something like this earlier, but I couldn't quite put the pieces together ><. What you really need to do is this:

Consider what the uncertainty in the radius is:\[r=3.1\times 10^4cm \pm 0.05cm\]The reason the uncertainty is this is because you could have anywhere from 3.05*10^4 to 3.15*10^4, and those numbers would be rounded to 3.1*10^4.

What you need to do is take the maximum value r COULD be (from uncertainty) and the minimum value r COULD be (from uncertainty), calculate the areas based on those radiuses and then take the difference between those values, which represents the total uncertainty in A, because it gives you the minimum and maximum values possible for A given the uncertainty.

Does that make sense?

Answer 25

^that makes sense... but it seems like we'd need to be given the uncertainty in the length - how are we to know it's +/- 0.5 cm vs +/- 1 cm? we aren't given how it's been measured... which is why i thought the question seemed to be missing that info in the first place. Hence my initial "erm... i guess maybe we're just doing it based on the significant figures...?"

Answer 26

I guess maybe we just have to assume it's accurate to +/- 0.5x10^3 cm...

Answer 27

I guess just assume maximum uncertainty.

Answer 28

thank you so much, I was thinking the same bc i had a similar problem with time but it is easy to find uncertainty because of the clue word "year", for this it doesnt state anything else, so how would i use something for reference, well just wanted to make sure you said that it is + or - 0.05cm ?