Question

what is relative error? what is the difference between absolute error and relative error?

Answer 1

Absolute error is the difference between the actual value of the physical quantity and the observed value. It is denoted by ε

ε = |x-x_obs| Where x = true value of the quantity and x_obs = observed value

Relative error is defined as the ratio of the absolute error to the true value of the quantity. It is denoted by η.

η= ε/x = |x-x_obs|/x

Suppose a voltage of a battery = 1.48V

But it was experimentally found to be 1.5V

Thus,

x = 1.48

x_obs=1.5

ε = |x-x_obs| = |1.48-1.5| =0.02V

Relative error is given by

η= ε/x = |x-x_obs|/x

η= 0.02/1.48 = 0.014

in terms of percentage it would be 1.4%

Differences

1. Absolute error has dimensions of the measured physical quantity while relative error is dimensionless.
2. Absolute error is difficult to find than relative error