Uncertainty in physical measurements

[O.J.]

i have some boubts about uncertainty in physical measurements. when adding two measurable values or subtracting them, we ADD UP the uncertainties-that is understood.

BUT when multiplying two measurable values WE ADD PERCENTAGE UNCERTAINTIES. Why is that?

 

[FredGarvin]

Have you ever taken a statistics class?

Take a quick read here:
http://www.rit.edu/~uphysics/uncertainties/Uncertainties.html

 

[scholzie]

Here's another uncertainties manual, also from RIT incidentally, with less theory than Vern's (which might not be what you're looking for, based on your original question) but with more emphasis on actually carrying through uncertainties with examples.

Richmond gave this to us in in print-out form during Physics I a few years back and it's a great guide: http://spiff.rit.edu/classes/phys273/uncert/uncert.html

 

[O.J.]

I still don't understand WHY multiplication of uncertainties requires ADDITION OF PERCENTAGES UNCERTAINTIES...

 

[DaveC426913]

I still don't understand WHY multiplication of uncertainties requires ADDITION OF PERCENTAGES UNCERTAINTIES...

Well, I haven't taken statistics but my intuition tells me:

If I have two numbers that have an uncertainty of 10%, and I multiply them together, will my uncertainty be 100%? That doesn't make sense does it?

Try it with 1 x 1. Your worst case is 0.81-1.21, not 0.0-2.0.

 

[O.J.]

what i need is a mathematical proof or a mathematical mechanism which proves the necessity to multiply uncertainties

 

[scholzie]

what i need is a mathematical proof or a mathematical mechanism which proves the necessity to multiply uncertainties

Well, then maybe you should read the document linked in the very first reply instead of demanding it be spoon-fed to you. It's written clear as day:

Derivation: We can derive the relation for multiplication easily. Take the largest values for x and y, that is
z + Dz = (x + Dx)(y + Dy) = xy + x Dy + y Dx + Dx Dy
Usually Dx << x and Dy << y so that the last term is much smaller than the other terms and can be neglected. Since z = xy,
Dz = y Dx + x Dy
which we write more compactly by forming the relative error, that is the ratio of Dz/z, namely
$$\frac{\Delta z}{z}=\frac{\Delta x}{x}+\frac{\Delta y}{y}+\cdot\cdot\cdot$$

The same document said it is often better to use standard deviations or analysis of covariance to do your error propagation.
A 5 minute Google search would http://www.physics.fsu.edu/users/ng/courses/phy2048c/lab/appendixI/App1.htm http://www.lhup.edu/~dsimanek/scenario/errorman/propagat.htm.

Since you're new to posting, I feel I should mention that many helpers here feel you should show an effort to help yourself at least as much as you expect to be helped. Plenty of people wish to help, but you got to put some elbow grease into it