A physical quantity `x` is calculated from the relation `x = ( a^(2) b^(3))/(c sqrt( d))`. If the percentage error in `a, b , c , and d are 2% , 1% , 3%, and 4%`, respectively , what is the percentage error in `x`?
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As `x = ( a^(2) b^(3))/(c sqrt( d))`, `:. (Delta x)/(x) = +- [ 2 ( Delta a )/a) + 3 ( Delta b)/(b) + (Delta c )/( c) + (1)/(2) (Delta d)/( d) ] (Delta x)/( x) xx 100` `= +- [ 2 xx 2% + 3 xx 1% + 3% + (1)/(2 )xx 4%]` `= +- [ 4% + 3% + 3% + 2% ] = +- 12%`.
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