Uncertainties in the measurements

Question 1

Difficulties that can be encountered when taking measurements using a ruler?

Answer 1

1. Zero Offset
2. Parallax Error
3. Fidelity of the scale
4. Calibration

Question 2

Zero Offset of a ruler?

Answer 2

the ruler needs to be placed such that the zero mark is as close as possible at the start of the item to be measured

Question 3

Parallax error of a ruler?

Answer 3

measure by viewing straight down at the marks

Question 4

Fidelity of the scale of a ruler?

Answer 4

are the graduations exactly 1 mm?

Question 5

Calibration of a ruler?

Answer 5

what is a true 1 mm?

Question 6

Rules for significant figures in a measurement?

Answer 6

• Rule 1: For numbers less than 1, we count the number of figures between the first non-zero figure and the last figure inclusive.
  
  • Example: 0.0010306 has five significant figures.
• Rule 2: For numbers greater than 10 and ending in a zero, we do not count the zero(s).
  
  • Example: 545000 has three significant figures.
• Rule 3: For numbers between 1 and 10 and with decimals consider the following example.
  
  • Example: 6.12 has three significant figures.

Question 7

Rules for calculations with significant figures?

Answer 7

• Rule 1 - When multiplying or dividing numbers: Identify the number in a calculation that is given to the least number of significant figures. Give the result of the calculation to the same number of significant figures.
  
  • Example: 3.7 x 3.01 = 11.137 As 3.7 has only two significant figures (least), then we should give the answer as 11.
• Rule 2 - When adding or subtracting numbers: Round the result of the calculation to the same number of decimal places as the number in the calculation given to the least number of decimal places.
  
  • Example: 11.24 + 13.1 = 24.34 Using rule 2, we should give the answer as 24.3.

Question 8

Types of Error?

Answer 8

• Systematic uncertainties
• Random uncertainties

Question 9

Examples of Systematic error?

Answer 9

• Constant (offset)
• Linearity Drift (or gain) – for example, due to temperature or aging effects
• Cyclic – for example, daytime cycle of temperature

Question 10

Examples of Random Uncertainties?

Answer 10

• Noise
• Rounding errors
• Reading errors Interference
• Power supply variations

Question 11

Graph showing Random Variation on a graph?

Answer 11

Question 12

Graph showing Random variation with systematic drift?

Answer 12

Question 13

What is the quantization error?

Answer 13

The Unavoidable loss of information

Question 14

Graphs showing how Quantised signal compares to original?

Answer 14

Question 15

What is the Precision of results?

Answer 15

A description of the spread in the results of repeated measurements

Question 16

What is the accuracy of results?

Answer 16

A measure of how close results are to the “true” values

Question 17

Using precision on a reuslts graph?

Answer 17

Question 18

Using accuracy on a results graph?

Answer 18