Question

how do i calculate a variable's uncertainty with another variable's uncertainty? and can the uncertainty be more that the value?

Answer 1

well i guess you've gotta cut down depending on the least significant figure?
i mean, if you do 4.0 + 5.394 it would equal to 9.394 , but that has to cut down to the variable that's least "accurate" aka 4.0, so you approximate 9.394 to the 0.1th
it would become 9.4 and that's that. i hope i helped.

Answer 2

well that might not be the right answer for my case but how do i calculate the uncertainty of one variable e.g. y when it is related this way y= mx + c, i do know the uncertainty and value of x, what should i do to find uncertainty of y? But thanks for the reply @LanHikari22!

Answer 3

Well someone needs to figure out cause im about to fail the test cause i only have to more minutes left

Answer 4

hmm, well i'm going to take a guess:
mx + c could be any point in said function y, so the certainty of y depends on (mx+c)
my information might be a bit shaky, i might need double-checking but let's consider this:
5.223 * 4.2 = 21.9366 , to measure the uncertainty of that we must consider the number with the least significant figures which is: 4.2, measuring from the very first significant measure; which is 4 we get 2 significant measures (4) and (.2) that allows the certainty to go up to 2 significant figured after the coma. (like 0.XX)
so we'd end up with an approximation of 5.223 * 42 = 21.94

back to your question, y depends on m, x and c
first evaluate mx, with the right uncertainty measure, then evaluate mx + c. also with the right uncertainty measure. and the uncertainty you get after all of this has to equal to the uncertainty of y. that's what i think. i'd ask you to double-check, if i made a mistake somewhere. i'd be glad if someone were to help

Answer 5

Well if you are taking a guess why are you needing help for..................................................So

Answer 6

@LanHikari22 thanks for help but I do understand that without the context will be tough for you to explain, really appreciate that someone bothers to explain this uncertainty and stuff!

Answer 7

so @TreyJones123 you have a better answer?

Answer 8

no it's just, i'm around 98% sure of myself but to be honest when it comes to physics i've never really given certainty much thought, so I might have some computation errors. look the certainty of y just has to be related to mx+c, just google "Certainty and significant figures Multiplication/Divison

Answer 9

also, no probs @iCurious i'm glad i could be of help.

Answer 10

@iCurious Well its my question and if i had an answer for it i would've not put it up nthere soooooooooooooooooooooooooo.........................

Answer 11

"how do i calculate a variable's uncertainty with another variable's uncertainty?"

You propagate the error with the appropriate formula (that come from statistics).

Foe example, if you have 5.0\(\pm\)2.0 m - 2.0\(\pm\)1.0 m= 3.0\(\pm \Delta z\)

then you use \(\Delta z=\sqrt{\Delta y^2+\Delta x^2}\)

\(\Delta z=\sqrt{2^2+\Delta 1^2}=2.236 \approx 2.2 \)

So your final answer is \(3.0\pm 2.2\) m

Answer 12

Are you familiar with Calculus? If so the the uncertainty in a quantity is related to the uncertainty in a variable that it depends on by the equation.\[\Delta y = \frac{ df }{ dx} \Delta x\] where
\[y = f(x)\]

An yes the uncertainly in y can be greater than that of x.

Answer 13

Yes again for the uncertainty in Y can be greater that the value of Y>

Now if y depends on several variables then
\[\Delta y = \sum_{i=1}^{n}\frac{ df }{ dx _{i}? }dx _{i}\]

where
\[\frac{ df }{dx _{i} }\] is the partial derivative of f with respect to xi

if the uncertainties in x are random as opposed to systematic then it is usually written that
\[\Delta y =\sqrt{\sum_{i=1}^{n}\frac{ df }{ dx _{i} }\Delta x _{i}}\]

Systematic errors are those that do not change with each measurement like errors in the calibration of instruments, using wrong parameter values in calculating the df/dx or not correcting for extraneous effects as the variation of barometric pressure with altitude.

Error estimation is very important in experimental physics for if the errors are not taken into account correctly the measurement may falsely support or not support a theory which is being tested by the measurement