Absolute and Relative Error Exercise Guide #1, True Value
Solve the following exercises
problem #1
The following table shows the results of measurements of a given length:
| Measurement | Measure |
| No. | cm |
| 1 2 3 4 5 6 7 |
2.83 2.85 2.87 2.84 2.86 2.84 2.86 |
Decide:
a) The probable value.
b) Relative and percentage error of the 3rd and 4th measurement.
Answer: a) 2.85 cm; b) 0.7% and 0.351%
problem #2
Given the length 3.2 ± 0.01, determine:
a) Relative error.
b) Percentage error.
Answer: a) 0.03; b) 3%
Problem #3
The percentage error of a measurement is 4%, if the length under study has a probable value of 1.85 m, determine:
a) Relative error.
b) Absolute error.
Answer: a) 0.04; b) 0.072m
Problem #4
If a body has a mass of 5 kg ± 0.02 kg and another of 0.09 kg ± 0.0021 kg, determine which of the two produces a greater error.
Answer: in the first
Problem #5
Knowing that the measurements of the sides of a rectangle are 73.3 ± 0.2 and 27.5 ± 0.2 in cm respectively, calculate the relative and percentage error of the surface and the perimeter.
Answer: Er = 0.01 and E% = 1%
Er = 0.001 and E% = 0.1%
Problem #6
Knowing that the measurement of the base of an equilateral triangle is 33.333 ± 0.003 cm, calculate the relative and percentage error of the surface and the perimeter.
Answer: Er = 0.00018 and E% = 0.018%
Er = 0.00003 and E% = 0.003%
Answer the following questionnaire
Question #1
Why do errors occur when taking measurements?
Question #2
What is meant by the true or probable value of a measurement?
