# Uncertainty in 1/x

Discussion in 'Mathematics' started by Newstein, Jan 17, 2019.

1. ### NewsteinNew commenter

If x = (10.0 +- 0.1) cm, 1/x = (0.10 +- ?)
I placed this qn in Science also.

2. ### NewsteinNew commenter

If y = 1/x,
dy/dx = - 1/x^2
mod delta y = (1/x^2) delta x
And for x = 10.0, delta y = (1/100) times 0.1 = 0.001
Sounds incorrect. Can uncertainty in 1/x be less than that of x?

3. ### gnulinuxOccasional commenter

Yes. You have more or less demonstrated that for x=10. What about for other values of x???

4. ### briancantOccasional commenter

Well I've had a couple of beers but you work out the percentage uncertainty of 1 and 10 and add them. Given their is no uncertainty in 1 and the percentage uncertainty in 10 is 1% the uncertainty in 0.1 is 1% of 0.1. So = 0.1 +- 0.001.

And if that make sense tomorrow I'll be amazed!!

5. ### NoSuchThingAsNormalNew commenter

The error is the same in the reciprocal as it is in x, surely?

x = 1 +/- 5%
1/x ~ 1 +/- 5%

6. ### briancantOccasional commenter

How does an absolute uncertainty of +-0.1 from a measurement of 10.0 equate to 5%? Surely this is 1%?