measurements: precision, accuracy and uncertainty
TRANSCRIPT
Measurements: Precision, Accuracy and Uncertainty
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
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…
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…
Practice
Measurement of Liquids
• Measure from the bottom of the meniscus
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
Convex Meniscus of Mercury
Practice
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)
Precision & Accuracy
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
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 ofSubstance 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
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
Other Units & Equivalences
• 1 t = 1 tonne = 103 kg
• 1 mL = 1 cm3 (cubic centimetres, cc)
• 103 L = 1 m3
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
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