1. Measurements
IS3

2. SI Units
Quantity SI unit Symbol
Mass kilogram kg
Length meter m
Time seconds s
Electric Current ampere A
Amount of
mole mol
substance
Temperature kelvin K

3. Fundamental and Derived Units
Quantity Symbol Base units
Volume m3 mxmxm
Speed ms−1 m/s
Force N kg x m/s2
Pressure Pa kg x m/s2 / m2
Converting Units:
• Speed of Light = 300000000 ms−1 = 3.0 x 108 ms−1
• Wavelength of blue light = 4.5 x 10−7 m = 0.00000045 m or 450 nm

4. Precision x Accuracy
• Accuracy: how close a measurement is to the ‘true’ value. Example:
True value: 9.87
Measurements: 9.86, 9.85, 9.89, 9.88, 9.87. 9.85, 9.86
• Precision: how close a measurement is to other measurements
True value: 9.87
Measurements: 6.86, 6.85, 6.89, 6.88, 6.87. 6.85, 6.86
An experiment may have great precision but be inaccurate

5. Associate each target with a normal curve:

6. Look at the numbers again…
Accuracy: how close a measurement is to the ‘true’ value. Example:
True value: 9.87
Measurements: 9.86, 9.85, 9.89, 9.88, 9.87. 9.85, 9.86
Precision: how close a measurement is to the other measurements
True value: 9.87
Measurements: 6.86, 6.85, 6.89, 6.88, 6.87. 6.85, 6.86
• What could be causing the variation observed in the measurements above?
• Which error can be easily reduced by simply repeating the measurement: the one associated
with precision or the one associated with accuracy?

7. Determining % error
• Remember the 2 sets of data from the previous slide.
Set 1: 9.86, 9.85, 9.89, 9.88, 9.87. 9.85, 9.86
Set 2: 6.86, 6.85, 6.89, 6.88, 6.87. 6.85, 6.86
• Knowing the true value is 9.87, find the % error of each set
• Step 1: find the mean of each set
– Set 1: 9.87
– Set 2: 6.87
• Divide the mean by the true value and multiply by 100:
– Set 1: 9.87/9.87 * 100 = 0%
– Set 2: 6.87/9.87 * 100 = 69.6%

8. Random x Systematic errors
• Random errors (affect precision)
A random error, is an error which affects a reading at random.
Sources of random errors include:
– The observer being less than perfect
– The readability of the equipment
– External effects on the observed item
• Systematic errors (affect accuracy)
A systematic error, is an error which occurs at each reading.
Sources of systematic errors include:
– The observer being less than perfect in the same way every time
– An instrument with a zero offset error
– An instrument that is improperly calibrated

9. Uncertainty
Absolute Uncertainty
• Room temperature = 22.5ºC ± 0.5
Percent Uncertainty
• Room temperature = 22.5ºC ± 2.2%

10. Determining the Uncertainty in Results
• For addition and subtraction, absolute
uncertainties may be added.
• For multiplication, division and powers,
percentage uncertainties may be added.

11. Error Bars
• Where relevant, uncertainties should be identified as error bars in plotted quantities.
Error bars may also reflect:
-Range of results
-Standard deviation
-etc…
Figure legend must be clear
about what error bar means.
How might the error bars
influence your interpretation
of the results displayed on a
graph?

12. Significant Figures
• The number of significant figures should reflect the
precision of the value of the input data.
e.g. 11.21 x 1.13 = 13.7883 => 13.8
• Least precise: 1.13 = 3 sig fig
e.g. 11.21 x 1.13 = 13.7883 => 13.8

13. Example