A quantity z, to be estimated has a dependency on the variables a, b and c as `z=ab^(2)c^(-2)`. The percentage of error in the measurement of a, b and c are respectively, 2.1% , 1.3% and 2.2% . The percentage of error in the measurement of z would then be

Options

A. `5.6%`
B. `1.6%`
C. `1.0%`
D. `9.1%`

Answer

D

Explanation

Given , `z=ab^(2)c^(-2)`
So, the percentage error in the volume is given by
`(Deltaz)/(z)xx100= [(Deltaa)/(a)+2 (Deltab)/(b)+2 (Delta c)/(c)] xx 100`
`=2.1%+2(1.3%)+2(2.2%)=9.1%`
So, the correct option is (d).