Question

Find the relative error in Z, if `Z =(A^(4)B^(1//3))/(CD^(3//2)` and the percentage error in the measurements of A,B,C and D are 4%,2%,3% and 1%, respectively.

Answer 1

`(DeltaZ)/(Z)=4((DeltaA)/(A))+(1)/(3)((DeltaB)/(B))+(DeltaC)/(C)+(3)/(2)((DeltaD)/(D))`
Given that, `(DeltaA)/(A)xx100=4,`
`(DeltaB)/(B)xx100=2,`
`(DeltaC)/(C)xx100=3,`
and `(DeltaD)/(D)xx100=1,`
`(DeltaZ)/(Z)xx100=(4xx4)+((1)/(3)xx2)+3+((3)/(2)xx1)`
`=16+(2)/(3)+3+(3)/(2)`
21.16%
The percentage error in the measurement of Z is 21.16% Therefore, the relative error in Z is 0.2116.