The Metric System Uncertainty in Measurements

System of Measurement English System – Traditionally used in the United States – Base units are interconverted with non- uniform conversion factors 12 inches = 1 foot 5280 feet = one mile 16 ounces = 1 pint 1 gallon = 4 quarts = 128 ounces 2

SI Units International System of Units – Système International d’Unités Internation agreement (1960) specifying a particular choice of metric units for use in scientific measurements A different base unit is used for each quantity. 3

Metric System Prefixes: - convert the base units into units that are appropriate for the item being measured - based on powers of ten - memorize these 4

What is the name given to the unit that equals a) 10 3 meters? b) second? c) mol? 5

What is the name given to the unit that equals a) 10 3 meters? b) second? c) mol? 6 kilometer nanosecond decimol

Length and Mass Length – the long dimension of an object – SI unit: meter (m) – similar to a yard Mass – a measure of the amount of material in an object – NOT the same as weight (the force that an object’s mass exerts due to gravity) – SI unit: kilogram (kg) ~2.2 pounds (lb) 7

Temperature -By definition, temperature is a measure of the average kinetic energy of the particles in a sample. -Physical property that determines the direction of heat flow -Heat flows from a substance at higher temperature to one at lower temperature 8

Temperature In scientific measurements, the Celsius and Kelvin scales are most often used. The Celsius scale is based on the properties of water. – 0  C is the freezing point of water. – 100  C is the boiling point of water. 9

Temperature The Fahrenheit scale is not used in scientific measurements.  F = 9/5(  C)

Volume Derived by taking length and cubing it The most commonly used metric units for volume are the liter (L) and the milliliter (mL). – A liter is a cube 1 dm long on each side. – A milliliter is a cube 1 cm long on each side. – SI unit: 1 m 3 11

We use 2 kinds of numbers in scientific work: 1)exact numbers – those whose values are known exactly - definition: 2.54 cm in an inch - counting: 14 people in the room 2) inexact numbers – those whose values have some uncertainty - numbers obtained by measurement (ALWAYS!) Uncertainty in Measurements 12

Uncertainty in Measurements Which of the following is an INEXACT number? a)number of people in this room b)number of milliseconds in one second c)length of a one dollar bill d)all of the above are inexact 13

Uncertainty in Measurements Different measuring devices have different uses and different degrees of accuracy. Uncertainty results from human errors and equipment errors. 14

Uncertainty in Measurements Uncertainty can be expressed in the form “measurement ± magnitude of uncertainty” - Example: mass of a dime is measured as ± g Instead, we drop the ± notation and just assume the last digit of a measurement is uncertain. 15

The smallest division marker is now 1 cm. So the only certain digit is 2 The last digit is obtained by estimating. So now we can only estimate to the tenths place. The reported length is 2.7 or 2.8 cm Uncertainty in Measurements 16. l l.... l l.... l 4.. cm Record the digits according to the smallest division markers (here, 0.1 cm). the first digit 2 plus the second digit 2.7 The last digit is obtained by estimating. The end of the line may be estimated between 2.7–2.8 as half way (0.5) or a little more (0.6), which gives a reported length of 2.75 cm or 2.76 cm. l 2 l 3 l 4 cm Certain digits

Accuracy versus Precision Accuracy refers to the proximity of a measurement to the true value of a quantity. Precision refers to the proximity of several measurements to each other. 17