# Homework Help: Uncertainty question

1. Oct 2, 2015

### Janiceleong26

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

2. Relevant equations
Absolute uncertainty in θ = δθ/θ

3. The attempt at a solution
I know that smaller θ gives smaller actual uncertainty, thus leaving B and D out. The answer is C. but what about option A?

2. Oct 2, 2015

### haruspex

If the fractional error in X is r, how large is the actual error in X? How large then is the actual error in theta?

3. Oct 4, 2015

### Janiceleong26

The actual error in X would be rX? And rθ?

4. Oct 4, 2015

### haruspex

Yes. So what is the fractional error in theta?

5. Oct 4, 2015

r ?

6. Oct 4, 2015

### haruspex

Right. Can you now see why A is wrong?

7. Oct 4, 2015

### Janiceleong26

No ..sorry..
If actual uncertainty in θ is r, then the percentage uncertainty of θ would be r x100 right? Isn't the effect the same?

8. Oct 5, 2015

### haruspex

No, the percentage uncertainty is 100x fractional uncertainty.

9. Oct 5, 2015

### Janiceleong26

What's the difference between fractional uncertainty and fractional error?

10. Oct 5, 2015

### haruspex

Sorry, I didn't notice I had switched from uncertainty to error. For the purposes of this question it makes no difference.
So in your post #5, you have that if the fractional (or percentage) uncertainty in x is r then the fractional (or percentage) uncertainty in theta is r.
Can you see how that conflicts with A?

11. Oct 5, 2015

### Janiceleong26

Ohhhh...is it because the percentage uncertainty would be the same for all values of θ, but the uncertainty itself varies?

12. Oct 5, 2015

### haruspex

Yes.

13. Oct 5, 2015

Thanks