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

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

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

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