Accuracy Precision Of Instruments And Errors In Measurement

To find the maximum percentage of error in the measurement of , where , we first need to understand how errors propagate in a formula involving multiple variables.

When dealing with functions of multiple variables, the percentage error in the result is the sum of the percentage errors contributed by each variable, each multiplied by the absolute value of the power to which that variable is raised in the expression.

The expression for is given by:

X = \frac{A^2B^{1/2}}{C^{1/3}D^3}

We can now write the formula for the percentage error in as follows:

Substituting the given percentage errors:

• 1\%\) for for for for

  Calculating each term:

  • 2 \times 1\% = 2\%
  • \frac{1}{2} \times 2\% = 1\%
  • \frac{1}{3} \times 3\% = 1\%
  • 3 \times 4\% = 12\%

  Summing up the percentage errors:

  2\% + 1\% + 1\% + 12\% = 16\%

  Hence, the maximum percentage of error in the measurement of is 16\% .