How to Determine Uncertainty for Pi Using Formulas and Calculus?

[FBS]

Homework Statement

Find the uncertainty for pi using (a) the formulas (b) calculus

Homework Equations

$$\pi$$ = (4$$/$$D$$^{2}$$)(hw - m$$/$$($$P$$L))

Uncertainty formulas:

for products and quotients:
Z = XY

$$\delta$$Z$$/$$Z = $$\delta$$X$$/$$X + $$\delta$$Y$$/$$Y

for differences:
Z = X - Y

$$\delta$$Z$$/$$Z = $$\delta$$X$$/$$(|X - Y|) + $$\delta$$Y$$/$$(|X - Y|)

The Attempt at a Solution

(a) using formulas:
I tried splitting up the equation into chunks, for example, making u = homework and v = $$P$$L but I seem to be heading towards a strangely complicated answer that doesn't resemble that of my classmates. Additionally, I'm not sure whether I am suppose to be applying the uncertainty formula for differences to this part of the original equation: (hw - m$$/$$($$P$$L))

(b) I have not gotten around to this part yet.

 

[gneill]

Yes, every mathematical operation needs to be "treated" to its uncertainty calculation.

There are six different variables in your formula, so evolving and simplifying the complete expression for the uncertainty is going to be quite an exercise in algebra.

I might suggest starting with the calculus method in order to see what you're working towards in the way of simplification. Have a lot of paper on hand.