1. Measurements: Precision, Accuracy and Uncertainty

2. Recording Measurements
Always record 1 more digit than the smallest division of the instrument
This last digit is an estimate so it is said to be uncertain. The ones before that are certain.
All measurements have a degree of uncertainty

3. Measurement of Distance
Top ruler
Smallest unit is 0.1 so it is 2.5something
Guess one more number (the “something”)
Could be 2.54 or 2.55 etc…

4. Measurement of Distance
Bottom ruler
Smallest unit is 1 so we know it is 2.something
Guess one more number (the “something)
Could be 2.4 or 2.5, etc…

5. Practice

6. Measurement of Liquids
Measure from the bottom of the meniscus

7. Measurement of Liquids
Mercury (Hg) has a convex meniscus (B), for which you would measure from the top
Concave/convex determined by surface tension between the liquid and the container

8. Convex Meniscus of Mercury

9. Practice

10. Precision & Accuracy
Precision measures the agreement between results of repeated measurements
i.e. how close measurements are to each other
More decimals = more precision!
Accuracy measures the agreement between a measurement and the accepted value
i.e. how close a measurement is to the accepted value (e.g. the speed of light is 2.998x108 m/s)

11. Precision & Accuracy

12. SI Units
The International System of Units (Le Système International d’Unités)
Modernized version of the metric system used in science
Any SI prefix can be used with any SI base unit

13. Equivalent Exponential
Some SI Units
SI Prefixes
Quantity
Unit name
Unit Symbol
Length
metre m
Mass
gram g
Volume
litre L
Time
second s
Temperature
kelvin K
Amount of
Substance
mole
mol
Written Prefix
Prefix Symbol
Equivalent Exponential
mega M
106
kilo k
103
hecto h
102
deka da
101 -
100
deci d
10-1
centi c
10-2
milli m
10-3
micro μ
10-6

14. Equivalent Exponential
SI Prefixes
5 Mm = 5x106 m
5 m = 5x10-6 Mm
1.2 ms = 1.2x10-3 s
12 s = 1.2x104 ms
Written Prefix
Prefix Symbol
Equivalent Exponential
mega M
106
kilo k
103
hecto h
102
deka da
101 -
100
deci d
10-1
centi c
10-2
milli m
10-3
micro μ
10-6

15. Other Units & Equivalences
1 t = 1 tonne = 103 kg
1 mL = 1 cm3 (cubic centimetres, cc)
103 L = 1 m3

16. Changing Units of Area & Volume
Example: 10 m3 = ? cm3
Start with the metric conversion factor
1 m = 100 cm
To get m3 we have to square both sides
(1 m)3 = (100 cm)3
Remember that the exponent applies to both the number and the units
13 m3 = 1003 cm3
1 m3 = 106 cm3

17. Changing Units of Area & Volume
10 m3 = ? cm3 We have just derived a conversion factor relating m3 and cm3 (1m3 = 106 cm3) Use this conversion factor to find the unknown just like before