Absolute Uncertainty of a Negative Power

[Redfire66]

1. Determine the relative and absolute uncertainties of R^-2 if R is measured to be 4.5 ± 0.005 m

2. The attempt at a solution
So according to what I know so far, multiplication and division of uncertainties requires the addition of relative uncertainties...

First I tried to get the relative uncertainty of R^-2. I assumed that a power of negative 2, that would be division twice (which I got to be 0.005/4.5 + 0.005/4.5 or just 2*(0.005/4.5)).

According to the CAPA answers, the resulting answer I got was the correct relative uncertainty of R^-2.
The relative uncertainty I got had a value of 2.3 x10^-3 or just 2x10^-3

But then when I tried to solve for the absolute uncertainty
I multiplied this to the value of 4.5
4.5^-2*2*(0.005/4.5)
= 1x10^-4 m^-2
However the the question posted on the CAPA problems tells me that my answer is incorrect. I'm not sure what I did wrong; the system didn't allow more than 1 digit so I rounded it down from 1.2

 

[BvU]

I don't know who CAPA is, but I'm on your side: relative error of .0011 in R, .0022 (not .0023 !?) in R², so .0022 in R^-2 as well.

R^-2 = .00494 and .0022 times that is .00011 (not .00012, though...).

That the system doesn't allow more than one digit is strange: it is a good habit to provide two digits if the first digit is a 1.

 

[Redfire66]

I don't know who CAPA is, but I'm on your side: relative error of .0011 in R, .0022 (not .0023 !?) in R², so .0022 in R^-2 as well.

R^-2 = .00494 and .0022 times that is .00011 (not .00012, though...).

That the system doesn't allow more than one digit is strange: it is a good habit to provide two digits if the first digit is a 1.

Okay. I see my mistake... I inputted 4.4 instead of 4.5 to get 0.0012; but since it was still 2x10^-3 the system gave me a correct answer for that part
I guess the program simply had the wrong answer since the only digit it wanted was the first one
Thanks for the help