A physcial quantity X is related to four measurable quantites a, b, c and d as follows : `X = a^2 b^3 c^(5//2) d^(-2)` The percentage error in the measurement of a, b, c and d are 1% , 2%, 3% and 4%, respectively. What is the percentage error in quantity X ? if the value of X calculated on the basis of the above relation is 2.763, to what value should you round off the result ?

Explanation

Here, `X = a^2 b^3 c^(5//2) d^(-2)`
`(DeltaX)/(X) = +- [2((Deltaa)/(a))+ 3((Delta b)/(b)) +(5)/(2)((Deltac)/(c )) + 2((Deltad)/(d))] = +- [2(1%) + 3(2%) + (5)/(2) (3%) + 2(4%)] = +- 23.5%`
Mean absolute error in `X = +- 0235 = +- 0.24,` rounding off to two digits. The value of X calculated on the basis of the above relation has to be rounded off so as to contain two significant digits. : x = 2.8