Let's say I have a measurement $x$ with an uncertainty $\Delta x$. I also have a constant $C$ which has no uncertainty.
I want to find the uncertainty of $y$, which is defined as $C/x$. How do I find the uncertainty $\Delta y$? I know that IF I instead defined $y = C*x$ then $\Delta y = C*\Delta x$, but I'm not sure how it would work for division?
Best Answer
For small $\Delta x$
$$y+\Delta y=\frac{C}{x+\Delta x} = \frac{C}{x(1+\Delta x/x)} = y(1+\Delta x/x)^{-1}=y(1-\Delta x/x) $$
So $\Delta y = -y\frac{\Delta x}{x}$
If $\Delta x$ is larger, for a specific $y$, a straightforward way is to work out $y$ in two cases, using $x + \Delta x$ and $x - \Delta x$ and see what $\Delta y$ results.