Determine the uncertainties

lavster

1. Homework Statement
what is the uncertainty of $$\frac{a+b}{c+d}$$ if a=b=c=d and $$σ_a = σ_b =σ_c=_d$$

2. Homework Equations

$$σ_{a+b}=√(σ_a^2+σ_b^2)$$

$$σ_{\frac{a}{b}}=√((\frac{σ_a}{a})^2+(\frac{σ_b}{b}^2))$$

3. The Attempt at a Solution
since a=b=c=d

$$σ_{a+b}=√2 σ_a$$

$$σ_{\frac{a}{b}}=√2 \frac{σ_a}{a}$$

so $$σ_{\frac{a+b}{c+d}} = \frac{√2 √2 σ _a}{2a} = \frac{σ_a}{a}$$

is this correct?!

Thanks

Last edited:
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gneill

Mentor
The result looks good to me!

lavster

Great thanks :) any idea why it is the same as the uncertainty in a single measurement... Just doesn't seem right to me! Xxx

BvU

Homework Helper
It is NOT the same as the uncertainty in a single measurement! That would be $\sigma_a$. Since you are evaluating a ratio, only relative errors matter. The factors $\sqrt 2$ and 2 just happen to cancel.

You can repeat the exercise with ${a+b+c}\over e+f+g$ and see what happens...

"Determine the uncertainties"

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