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Question

Relative error in Z, given that Z = 1/A2 is________


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Solution

Relative error:

  1. The ratio of the absolute error of a measurement to the measurement being taken.
  2. This type of error is relative to the size of the item being measured.
  3. The relative error is expressed as a percentage.
  4. It has no units.
  5. If the true measurement of the object is not known, then the relative error can be found using the measured value.

Step 1: Given information:

Z=1A2

Step 2: Formula to calculate relative error:

Relativeerror=x0-x/x=x/x.

where

x0= measured value

x= actual value

x= absolute error

Step 3: To find the relative error in Z.

We have Z=1A2

so now take log on both side

logZ=log1A2

Differentiating both sides with respect to dZ.

1Z×dZdZ=dA-2dZ1Z=±-2×1A×dAdZdZZ=±-2×dAAdZZ=2×dAA

Hence, the relative error in Z is dZZ is two times the relative error in A that is dAA.


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