A question on percentage uncertainty

[Mr Bob555]

Homework Statement

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 .

Homework Equations

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 doesn't 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%.

 

[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?

 

[Mr Bob555]

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?

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

 

[Mr Bob555]

Anyone else?

 

[Simon Bridge]

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