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A measurement of length is recorded as 12.3 cm with an uncertainty of ±0.1 cm. W

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Question: A measurement of length is recorded as 12.3 cm with an uncertainty of ±0.1 cm. What is the relative error in the measurement?

Options:

  1. 0.0081
  2. 0.008
  3. 0.01
  4. 0.1

Correct Answer: 0.008

Solution: 

Relative error = (absolute error / measured value) = 0.1 / 12.3 = 0.0081.

A measurement of length is recorded as 12.3 cm with an uncertainty of ±0.1 cm. W

Practice Questions

Q1
A measurement of length is recorded as 12.3 cm with an uncertainty of ±0.1 cm. What is the relative error in the measurement?
  1. 0.0081
  2. 0.008
  3. 0.01
  4. 0.1

Questions & Step-by-Step Solutions

A measurement of length is recorded as 12.3 cm with an uncertainty of ±0.1 cm. What is the relative error in the measurement?
  • Step 1: Identify the absolute error, which is given as ±0.1 cm.
  • Step 2: Identify the measured value, which is 12.3 cm.
  • Step 3: Use the formula for relative error: Relative error = (absolute error / measured value).
  • Step 4: Substitute the values into the formula: Relative error = 0.1 / 12.3.
  • Step 5: Calculate the result: 0.1 divided by 12.3 equals approximately 0.0081.
  • Relative Error – Relative error is the ratio of the absolute error to the measured value, expressed as a fraction or percentage.
  • Absolute Error – Absolute error is the uncertainty in a measurement, representing the range of possible values.
  • Measurement Uncertainty – Measurement uncertainty indicates the doubt about the result of a measurement, often expressed as ± value.
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