Errors and Measurements

# Absolute and Relative Error Exercise Guide #1, True Value

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?