Explain the propagation of errors in multiplication.

Explanation

Error in the product of two quantities: Let `Delta `A and `Delta ` B be the absolute errors in the two quantities A, and B, respectively. Consider the product Z=AB .
The error `Delta Z` in Z is given by `Z pm Delta Z = (A pm Delta A) (B pm Delta B)`
Dividing LHS by Z and R.H.S by AB, we get,
`1 pm (Delta Z)/(Z ) = 1 pm (Delta B)/(B) pm (Delta A)/(A) pm (Delta A)/(A) . (Delta B)/(B)`
As ` Delta A// A, Delta B//B` are both small quantities, their product term `(Delta A)/(A) . (Delta B)/(B)` can be neglected . the maximum fractional error in Z is
`(Delta Z)/(Z) = pm ( (Delta A)/( A) + (Delta B)/( B) )`