Worksheet: Measurement Error

In this worksheet, we will practice defining and calculating the absolute and relative errors of measured values.

Q1:

In an experiment, the speed of sound waves on Earth at sea level at a temperature of 21C is 333 m/s. Find the percent relative error in the measurement using an accepted value of 344 m/s. Give your answer to one decimal place.

  • A2.3%
  • B1.0%
  • C3.4%
  • D4.4%
  • E3.2%

Q2:

Which of the following is the correct formula for the value of the relative error of the measurement 𝑟 given the accepted value, 𝑥, and the absolute error, Δ𝑥?

  • A𝑟=Δ𝑥𝑥
  • B𝑟=𝑥Δ𝑥
  • C𝑟=𝑥+Δ𝑥
  • D𝑟=|𝑥Δ𝑥|
  • E𝑟=𝑥Δ𝑥

Q3:

An experimental apparatus for measuring the acceleration due to gravity produces an absolute error of 0.05 m/s2. The apparatus is used on two different planets. One planet has an accepted value for its gravitational acceleration of 3.72 m/s2 and the other has an accepted value for its gravitational acceleration of 8.87 m/s2. Find the difference between the percent relative errors of the measurements of gravitational acceleration made by the apparatus on the two planets. Give your answer to one decimal place.

  • A0.8%
  • B8.0%
  • C0.3%
  • D2.6%
  • E2.5%

Q4:

Which of the following is the correct formula for the value of the relative error of the measurement 𝑟 given the accepted value, 𝑥 and the measured value, 𝑥?

  • A𝑟=(𝑥𝑥)𝑥
  • B𝑟=𝑥(𝑥𝑥)
  • C𝑟=𝑥|𝑥𝑥|
  • D𝑟=|𝑥𝑥|𝑥
  • E𝑟=|𝑥𝑥|𝑥

Q5:

In an experiment, the atmospheric pressure at sea level on Earth is measured to be 101,150 Pa. Find the absolute error in the measurement using an accepted value of 101,325 Pa.

Q6:

In an experiment, the acceleration due to gravity at the surface of the Earth is measured to be 9.90 m/s2. Find the absolute error in the measurement using an accepted value of 9.81 m/s2.

Q7:

Which of the following is the correct definition of the accepted, or actual, value of a quantity?

  • AThe most recently measured value of the quantity
  • BThe value of the quantity the first time it was ever measured
  • CThe average measured value of the quantity
  • DThe value of the quantity when it is not altered by any measurement errors
  • EThe value of the quantity that occurs most frequently when the value is measured

Q8:

In an experiment, the density of pure water at sea level on Earth at a temperature of 0C is 997.5 kg/m3. Find the percent relative error in the measurement using an accepted value of 1,000 kg/m3. Give your answer to one decimal place.

  • A1.0%
  • B0.4%
  • C0.2%
  • D5.0%
  • E0.3%

Q9:

Which of the following is the correct formula for the value of the absolute error of a measurement, Δ𝑥, given the accepted value, 𝑥, and the measured value, 𝑥?

  • AΔ𝑥=𝑥𝑥
  • BΔ𝑥=𝑥𝑥
  • CΔ𝑥=𝑥𝑥
  • DΔ𝑥=𝑥𝑥
  • EΔ𝑥=|𝑥𝑥|

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