# Uncertainty power rule

## Homework Statement

D= A +/-ΔA
D= 5.160 +/- 0.01 cm

D^2= 26.6 +/- 0.1 cm^2

## Homework Equations

for the power rule uncertainty
:
A ((ΔA/A) + (ΔA/A) )
So then its (5.160)( (0.01/5.16)(2)) = 0.004

## The Attempt at a Solution

im getting 0.004 as the absolute uncertainty but the uncertainty calculator i found online gives me 0.1 .
is my formula wrong?

## Answers and Replies

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gneill
Mentor
For the uncertainty as a result of a power in general, let Q = xn and δx be the uncertainty in x. Then
$$\frac{\delta Q}{|Q|} = |n| \frac{\delta x}{|x|}$$
In your case the power is n = 2 and x is a positive value, so that δQ becomes:
$$\delta Q = 2 x^2 \frac{\delta x}{x} = 2 x \delta x$$
Your formula A ((ΔA/A) + (ΔA/A) ) should have been A2 ((ΔA/A) + (ΔA/A) ).

For the uncertainty as a result of a power in general, let Q = xn and δx be the uncertainty in x. Then
$$\frac{\delta Q}{|Q|} = |n| \frac{\delta x}{|x|}$$
In your case the power is n = 2 and x is a positive value, so that δQ becomes:
$$\delta Q = 2 x^2 \frac{\delta x}{x} = 2 x \delta x$$
Your formula A ((ΔA/A) + (ΔA/A) ) should have been A2 ((ΔA/A) + (ΔA/A) ).
oh ok. so that is what i did wrong. I got it now. THANK YOU SO MUCH.!!

To make this problem simple, see D² as D * D.

Well, the rule for finding the uncertainty in multiplication is Δw = √((yΔx)² + (xΔy)²), coming from w = xy. It's the simpler similar version of the formula other user uses.

Now, you try to use that formula.

To make this problem simple, see D² as D * D.

Well, the rule for finding the uncertainty in multiplication is Δw = √((yΔx)² + (xΔy)²), coming from w = xy. It's the simpler similar version of the formula other user uses.

Now, you try to use that formula.
using this equation, gives me 0.0729, whereas the previous one i used gives me 0.1032.
so, i can conclude that Δw = √((yΔx)² + (xΔy)²) formula gives me more precise uncertainty?