# Specific Case: Uncertainties

1. Sep 20, 2007

### lapo3399

For the following calculation, would the uncertainty propagate as I have estimated?

$$\frac{\left(a \pm \Delta a \right) + \left(b \pm \Delta b \right)}{\left(c \pm \Delta c \right) \cdot \left(d \pm \Delta d \right)} = \frac{a+b}{cd} \pm \frac{a+b}{cd} \left( \frac{\Delta a + \Delta b}{a + b} + \frac{\Delta c}{c} + \frac{\Delta d}{d} \right)$$

Thanks.

2. Sep 20, 2007

### learningphysics

Yes, looks good to me.

3. Sep 20, 2007

### lapo3399

Thanks!

One more quick question - is the following uncertainty propagation correct also?

$$\frac{1}{ \left( r \pm \Delta r \right)} = \frac{1}{r} \pm \frac{1}{ \Delta r}$$

Thanks again.

4. Sep 20, 2007

### learningphysics

That doesn't look right to me. To get the relative uncertainty of the fraction... add the relative uncertainty of the top (0)... to the relative uncertainty of the bottom...

So the relative uncertainty of the fraction seems to be $$\frac{\Delta r}{r}$$ so the absolute uncertainty would be $$\frac{1}{r}\times \frac{\Delta r}{r}$$