Relative uncertainty (negative exponent)

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SUMMARY

The relative uncertainty of a measured distance R, given as 3.400±0.003m, is calculated to be 8.8×10-4. When determining the relative uncertainty for R-2, the calculation yields -1.76×10-3. However, the negative sign is disregarded as relative uncertainty is always expressed as a positive value, indicating that the magnitude should be taken into account. Thus, the correct relative uncertainty for R-2 is 1.76×10-3.

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Homework Statement


A distance R is measured to be 3.400±0.003m. What is the relative uncertainty in R? 9×10-4
What is the relative uncertainty in R^-2?

Homework Equations

The Attempt at a Solution


Relative uncertainty of R is 0.003/3.4=8.8e-4
Relative uncertainty of R^-2= -2(8.8e-4)=-1.76e-3?
How do you calculate relative uncertainty with a negative exponent?
 
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The relative uncertainy is always positive. The negative sign in your calculation indicates that a larger R leads to a smaller R-2, but that is not relevant here, so you have to take the magnitude.
 
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mfb said:
The relative uncertainy is always positive. The negative sign in your calculation indicates that a larger R leads to a smaller R-2, but that is not relevant here, so you have to take the magnitude.
Thank you!
 

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