Say I have measured the value
A = 50 +- 2
and from this I am calculating the value:
B(A) = A^2
From what I understand I calculate the new error using error propagation to be
delta_B = dB/dA * delta_A = 2*A*delta_A = 2*50*2 = 200
A has a therefore relative error of
2/50 = 4%, but
B has a relative error of
200/2500 = 8%.
Shouldn't the relative error stay the same? It seems illogical, that a simple arithmetic calculation would change the relative error of the value.
Or am I doing something very wrong?