# Error progrigation

1. Jan 21, 2008

### dionysian

Error propagation

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

$$\frac{ - \frac{R_{2}}{R_{1}}}{1 + \frac{1}{A} + \frac{R_{2}}{A R_{1}}}$$

2. Relevant equations

$$R_{1} = 10000 \pm 5 \%$$
$$R_{2} = 10000 \pm 5 \%$$
$$A = 1000$$

3. The attempt at a solution

I try to follow the example of at the website http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart1.html [Broken] and in there example
$$x = ( 2.0 \pm 0.2)$$
$$y = (3.0 \pm 0.6)$$
$$z = \frac{x}{y}$$

This is what they do in their example:
$$z = \frac{2.0}{3.0} = 0.6667$$
$$\Delta z = 0.3 (0.6667 ) = 0.2$$
$$z = (0.7 \pm 0.2)$$

Now what i dont realy understand is where they get $$0.3$$ from?
It seems that they just divide the uncertainty $$\frac{0.2}{0.6} = .33$$.

But, if i do this in my example i get $$\frac{500}{500} = 1$$. Then when i multiply this agianst $$\frac{10000}{10000} = 1$$ i get 100% error. Yikes!

I kind of feel embarrassed asking this because i should have learned this a long time ago in physics but it was one of those things i never really took the time to actually understand.

Last edited by a moderator: May 3, 2017
2. Jan 21, 2008

### hage567

The 0.3 comes from the addition of the relative errors of x and y. Find equation 2a on that page.

3. Jan 22, 2008

### dionysian

Thank you sir