# What would my uncertainty be with these 2 values?

#### nukeman

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

I am doing percent difference of 2 values.

value 1 = .013329 +- .001 cm
value 2 = .013331 +- .001 cm

So, for percent difference I do:

.013331 - .013329 / ((.013331 + .013329)/2)

gives me .015%, but what would my uncertainty be? I don't wuite understand. Thanks!

2. Relevant equations

3. The attempt at a solution

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#### tal444

I believe when you divide or multiply numbers, the uncertainly is the sum of the uncertainty in your original numbers.

#### gneill

Mentor
Percent difference between two values a and b can be written as a function of the two variables a and b:

$p(a,b) = \frac{b - a}{b}100$

If its variables have independent associated errors Δa and Δb, then the error in the function, Δp, can be obtained using partial derivatives of the function w.r.t. those variables, so that:

$\Delta p^2 = \left| \frac{\partial p}{\partial a}\right|^2 \Delta a^2 + \left| \frac{\partial p}{\partial b}\right|^2 \Delta b^2$

You can do the same for functions of any number of variables, f(a,b,c,...). All you need to be able to do is take partial derivatives of the function w.r.t. each of its variables.

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