# Uncertainty propagation

1. Feb 5, 2008

### glasshut137

1. The problem statement, all variables and given/known data

Calculate "f" and its uncertainty, watch the units, show all work.

2. Relevant equations

f(x,z)= z/x
x=100.5(+ or -) 3.8 cm
y=71(+ or -) 1 s

3. The attempt at a solution

ok so i know that to find uncertainty i have to use the equation delta f(x,y)=df(x,y)/dx *(delta x) + df(x,y)/dy * delta y. I got (delta f)= z*lnx*(delta x) + (delta z)/x. When i plug in the numbers the units dont match up, i get cm*s + s/cm.

2. Feb 5, 2008

### Hootenanny

Staff Emeritus
That is not correct. In general:

$$\left(\Delta f(x,y)\right)^2 = \left(\frac{\partial f}{\partial x}\right)^2\Delta x^2 + \left(\frac{\partial f}{\partial y}\right)^2\Delta y^2$$

This is also in correct.

$$\frac{d}{dx}\left(\frac{1}{x}\right) \neq \ln|x|$$

Last edited: Feb 5, 2008
3. Feb 5, 2008

### glasshut137

oh jeez you're right thanks

4. Feb 5, 2008

### Hootenanny

Staff Emeritus
Take a note of my further comment, which was added after you replied.