# Finding the uncertainty

1. Feb 5, 2012

### carloz

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

M = (a-b)/2 + a

a = 15
b=5

What is the uncertainty in M if the uncertainty in a and b is ±0.7?

2. Relevant equations

for c = a + b
Error in c =√[(error in a)^2 + (error in b)^2]

3. The attempt at a solution

Error in M = √[0.7^2 * 3] = 1.2124

The problem I am having is that we learn that the above formula can only work when the errors are independent of one another. the error in a is obviously not independent of the error in a. so i think i'm wrong.

What do you think?

Thank you.

2. Feb 5, 2012

### rock.freak667

If I remember correctly, the errors work like this:

s= a+b ⇒ Δs=Δa + Δb

s= a-b ⇒ Δs= Δa + Δb

s=ab ⇒ Δs/s = Δa/a + Δb/b

So you can apply the first two as needed.

3. Feb 5, 2012

### carloz

yes. but that only works when the uncertainties in a and b are independent. however in my equation for M, a appears twice. since the error of a is not independent of a, how do i go about finding the uncertainty?

thanks.

4. Mar 15, 2012

### shfreeman

Why not just simplify your problem

(a-b)/2+a

into

(3a-b)/2

and then use the rules for the error of 3a+b. You don't need to worry about the independency of error a to error a.
This way I get

(3 Δa + Δb)/2 = 1.4

Or using the other rule [ √(Δa2 + Δb2) ]

( √(9*Δa2 + Δb2) ) / 2 ≈ 1.1068