measurements: precision, accuracy and uncertainty

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