A physical eqantity X is related to four measurable quantities 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 ralation is `2.763`, to what value should you round off the result.

Explanation

Given, physical quantity is `X=a^2b^3c^((5)/(2))d^-2`
Maximum percentage error in X is
`(triangleX)/(X)xx100=+-[2((trianglea)/a)xx100)+3((triangleb)/(b)xx100)`
`+(5)/(2)((trianglec)/(c)xx100)+2((triangled)/(d)xx100)]`
`=+-[2(1)+3(2)+(5)/(2)(3)+2(4)]%`
`=+-[2+6+(15)/(2)+8]=+-23.5%`
Percentage error in quantity `X=+-23.5%`
Mean absolute error in `X=+-0.235=+-0.24`(rounding off up to two significant digits)
The calculated value of x should be round-off up to two significant digits.
`X=2.8`