# A question on percentage uncertainty

1. May 24, 2016

### Mr Bob555

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

Say we have the equation D2 = C x N where C = A2.
Using a graphical method to find the % uncertainty of C (from graph of D2 against N) which involves working out the gradient which equals C and so forth. This value is 25%.
The question is "what is the percentage uncertainty of A?"

This is actually a question that appeared in an A-level paper i did today and it was the only one that really bamboozled me .
2. Relevant equations

3. The attempt at a solution
I realize you don't divide by two;my reasoning being that when asked to calculate the % uncertainty of r in say the equation V = 4/3 x π x r3 the question doesnt explicitly state r3.

So i think that it is between doubling 25% or just leaving it. Now i think it was the latter but in the exam I did indeed double it to 50%.

2. May 24, 2016

### Simon Bridge

You are propagating errors of form $z=x^a$ knowing $x\pm xp_x/100$ where $p_x$ is the known percentage error.
So what is the rule for propagating the error on a power?

3. May 24, 2016

### Mr Bob555

Multiply the percentage uncertainty by whatever the variable is to the order of?

4. May 24, 2016

### Mr Bob555

Anyone else?

5. May 25, 2016

### Simon Bridge

What's wrong with the reply you got so far?