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Uncertainties( Raising to a fractional power)

I know that if value a is raised to the power n then the percentage uncertainty = n*(delta a/a)*100 but what if n = 1/k (k where is any number greater than 1). What do i do?

(edited 11 years ago)

Reply 1

Stonebridge

Original post by SorryInAdvance

I know that if value a is raised to the power n then the percentage uncertainty = n*(delta a/a)*100 but what if n = 1/k (k where is any number greater than 1). What do i do?

It's still times n.
If you have a square root (power half) then the % uncertainty is halved.

Reply 2

SorryInAdvance

Original post by Stonebridge

It's still times n.
If you have a square root (power half) then the % uncertainty is halved.

Does logs affect the value?

Reply 3

Stonebridge

Original post by SorryInAdvance

Does logs affect the value?

Yes.
If you have log_e of a number N with an uncertainty ±n it's done as follows
x = log_e (N ± n)
Gives Log_eN ± n/N

So if you have a length measured as, say, 50m ± 2m
Then the uncertainty in the log_e is just 2/50
Giving Log_e(50) ± 2/50
Giving 3.91 ± 0.04