Uncertainty Problem

1. Sep 19, 2009

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 ive attempted to use millimeters, centimeters, meters and even kilometers.

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

Last edited: Sep 19, 2009
2. Sep 19, 2009

Redbelly98

Staff Emeritus
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.

3. Sep 19, 2009

anwarjackson

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

4. Sep 19, 2010

waleed123

hey how did u get (1/4)

help me

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

5. Sep 19, 2010

Redbelly98

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

6. Sep 19, 2010

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

7. Sep 20, 2010

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.