Propagation of Errors
Propagation of Errors.
(1) Error in sum of the quantities : Suppose z = x + y
Let
Δx = absolute error in measurement of x
Δy = absolute error in measurement of y
Δz = absolute error in calculation of z
The maximum absolute error in z is
Percentage error in the value of
(2) Error in difference of the quantities : Suppose z = x – y
Let
Δx = absolute error in measurement of x,
Δy = absolute error in measurement of y
Δz = absolute error in calculation of z.
The maximum absolute error in z is
Percentage error in the value of
(3) Error in product of quantities : Suppose z = x ´ y
Let
Δx = absolute error in measurement of x,
Δy = absolute error in measurement of y
Δz = absolute error in calculation of z.
The maximum fractional error in z is
Percentage error in the value of z = (Percentage error in value of x) + (Percentage error in value of y)
(4) Error in division of quantities : Suppose z=x / y
Let
Δz = absolute error in measurement of z,
Δx = absolute error in measurement of x
Δy = absolute error in calculation of y.
The maximum fractional error in z is
Percentage error in the value of z = (Percentage error in value of x) + (Percentage error in value of y)
(5) Error in quantity raised to some power : Suppose
Let
Δx = absolute error in measurement of x,
Δy = absolute error in measurement of y
Δz = absolute error in calculation of z
The maximum fractional error in z is
Percentage error in the value of z = n (Percentage error in value of x) + m (Percentage error in value of y)