Quick question about uncertainty calculation

[mjolnir80]

Homework Statement

lets say we have A * B
A=12.8 + 0.2
B=3.75 + 0.08
how would we calculate the new uncertainty value
ive seen soo many ways of doing this I am a bit confused
thanks in advance

Homework Equations

any equation used to calculate uncertainty

The Attempt at a Solution

the 2 main ways I've seen is one involving partial dervatives and the other is taking the square root of the answer times the (uncertainties/value)²
im a little confused about which one to use

 

[rock.freak667]

If C=AB, then

$$\frac{\delta C}{C}=\frac{\delta A}{A}+ \frac{\delta B}{B}$$


this is obtained using differential calculus.

 

[granpa]

(A+ε₁)*(B+ε₂)
AB+Aε₂+Bε₁+ε₁ε₂

so if we disregard the final term the incertainty would be Aε₂+Bε₁

partial derivative of AB with respect to A is B
partial derivative of AB with respect to B is A

does that help?

 

[granpa]

If C=AB, then

$$\frac{\delta C}{C}=\frac{\delta A}{A}+ \frac{\delta B}{B}$$


this is obtained using differential calculus.

whats that called? I want to look that up. it looks interesting.

 

[granpa]

nevermind I found it.looks like the derivative rule is the most general.

if the uncertainties are independent you can take the square root of the sum of the squares of the partial derivatives times the uncertainties. that would be probable error not maximum error though.

http://web.mit.edu/fluids-modules/www/exper_techniques/2.Propagation_of_Uncertaint.pdf