Error in the product of two quantities:
Let ∆A and ∆B be the absolute errors in the two quantities A, and B, respectively. Consider the product Z = AB,
The error AZ in Z is given by Z ± AZ = (A ± ∆A) (B ± ∆B)
= (AB) ± (A ∆ B) ± (B ∆ A) ± (∆A • ∆B)
Dividing L.H.S by Z and R.H.S by AB, we get,
As ∆A/A, ∆B/B are both small quantities, their product term \(\frac{ΔA}{A}. \frac{ΔB}{B}\) can be neglected.
The maximum fractional error is Z is
\(\frac{ΔZ}{Z}\) = ± (\(\frac{ΔA}{A}\) + \(\frac{ΔB}{B}\))
