Simple Experimental Error Problem

[Lavace]

I have two values:

r = 12.3 ± 0.2m
d = 0.57 ± 0.03mm

I want to divide the two values to find theta (d/r = theta), how do I go about this?
I assume that I add the experimental error margins together after the division of 12.3 and 0.57? Giving me:

4.63 x 10^-5 ± 2.0003m

 

[kuruman]

I cannot figure out what you've done here but 2.0003 m does not look like an appropriate uncertainty for an angle. The way this is usually done is through fractional uncertainties. The fractional uncertainty for the radius is

$$\delta_{r}= \frac{\delta r}{r} = \frac{0.2}{12.3}$$

and for the arclength

$$\delta_{d}= \frac{\delta d}{d} = \frac{0.03}{0.57}$$

Then the fractional uncertainty for the angle is

$$\frac{\delta\theta}{\theta} = \sqrt{\delta^{2}_{r}+\delta^{2}_{d}}$$

 

[Kurdt]

For division of variables on would normally treat the erros like so.

$$\frac{\delta q}{q} = \sqrt{\left(\frac{\delta r}{r}\right)^2 + \left(\frac{\delta d}{d}\right)^2}$$