# A physical quantity X is related to four measurable quantities a, b, c and d as follows:

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A physical quantity X is related to four measurable quantities a, b, c and d as follows:

X = a2 b3 c5/2 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.

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The fractional error in X is

dX/X = 2da/a + 3db/b + 2.5dc/c + 2d(d)/d

= 0.235 ≃ 0.24

Since the error is in first decimal, hence the result should be rounded off as 2.8.