Question

if x has been measured as 4.0+-0.1 cm, what should I report for x^2 and x^3?

Answer 1

lets say we measure some quantity Q to some tolerance d to get Q = x +/- d
then maximum Q^2 would be (x + d)^2 = x^2 + 2xd + d^2
and minimum Q^2 would be (x - d)^2 = x^2 -2xd + d^2
so Q^2 = x^2 + (d^2 +/- 2xd)

does that make sense to you?

Answer 2

so in my case, how would you work that out?

Answer 3

x^2 = (4.0)^2 + ((0.1)^2 +/- 2*4.0*0.1)

Answer 4

x^2 = 16.0 - 0.79 to 16.0 + 0.81