Error Propagation: Calculating Uncertainty of a Ratio

[dionysian]

Error propagation

Homework Statement

Calculate:

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

Homework Equations

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

The Attempt at a Solution

I try to follow the example of at the website http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart1.html 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 don't really 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.

 

[hage567]

Now what i don't really understand is where they get from?
It seems that they just divide the uncertainty

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

 

[dionysian]

Thank you sir