Explain the propagation of errors in multiplication.

1.	Explain the propagation of errors in multiplication.
Answer» SOLUTION :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 pmDelta Z = (A pmDelta A) (B pmDelta B)` Dividing LHSby 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) )`

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