How to Calculate the Absolute Uncertainty in Distance Measurement?

[anwarjackson]

A distance R is measured to be 4.000±0.006 m. What is the absolute uncertainty in R to the power of negative two?

Here is what i tried, apparently my units are not correct, if anyone can suggest the porper units that would be much appreciated.

let x be uncertainty of R^-2,
let y be uncertainty of R
let n be raised power (in this case -2)x = n(R^n-1)y
= 2 (1/4)0.006
= 0.003

What am I doing wrong? Question was posted on the CAPA problem sets for my physics class, CAPA keeps saying improper units however I've attempted to use millimeters, centimeters, meters and even kilometers.

Therefore, uncertainty of R^-2 is 0.0625 ± 0.003 m

 

[Redbelly98]

If R has units of m, then:

R^2 has units of ___?
1/R^2 has units of ___?

p.s. 0.003 would be the relative uncertainty, not the absolute uncertainty.

 

[anwarjackson]

WOW, thanks I wasn't thinking of that, I've been awake for too long apparently.

 

[waleed123]

hey how did u get (1/4)

help me

my values are (3.000+- 0.002) samw ques capa

 

[Redbelly98]

Welcome to Physics Forums. What do you know about calculating uncertainties?

 

[waleed123]

its cool man i got the ans after like 2mint i posted the thing...i did it in my own method..same result thanks anyways

 

[RoyalCat]

You had the formula right, and the units don't quite matter, as long as you're using the same units for $$R$$ and $$\Delta R$$ when you plug them into your formula.

Your formula is correct too, only you plugged in n=-2 in one place, and n=0 in the other!

x=nR^(n-1) y
Plugging in n=-2, and ignoring the negative sign we get for x, since it is an uncertainty:
x=2R^(-3) y
4^-3 is not 1/4.