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Determine the uncertainties

  • Thread starter lavster
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1. Homework Statement
what is the uncertainty of [tex] \frac{a+b}{c+d} [/tex] if a=b=c=d and [tex] σ_a = σ_b =σ_c=_d [/tex]


2. Homework Equations

[tex] σ_{a+b}=√(σ_a^2+σ_b^2) [/tex]

[tex] σ_{\frac{a}{b}}=√((\frac{σ_a}{a})^2+(\frac{σ_b}{b}^2)) [/tex]

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

[tex]
σ_{a+b}=√2 σ_a [/tex]

[tex] σ_{\frac{a}{b}}=√2 \frac{σ_a}{a} [/tex]

so [tex] σ_{\frac{a+b}{c+d}} = \frac{√2 √2 σ _a}{2a} = \frac{σ_a}{a} [/tex]

is this correct?!

Thanks
 
Last edited:

gneill

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The result looks good to me!
 
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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

Science Advisor
Homework Helper
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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...
 

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