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Measurements 1 Nature of Measurement Measurement - quantitative observation consisting of 2 parts Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63 10-34 Joule seconds 2 International System (le Système International) Based on metric system and units derived from metric system. 3 The Fundamental SI Units 4 Dimensional Analysis or The Unit Factor Method Proper use of “unit factors” leads to proper units in your answer. Unit Factor means the ratio equals 1. Multiplying by 1 changes nothing mathematically. Have X Wanted/Have = Wanted Where Wanted/Have = 1 or unity 5 Unit Factor Practice 1. Convert 34.5 centimeters into inches (2.54cm/1 in). 34.5 cm x 1.00 in/2.54 cm = 13.5826771653 inches Since original measurement is good to 3 digits, we end up with 13.6 in. 2. Convert 2376 grams into kilograms. 2376 g x 1 kg/1000g = 2.376 kg 3. Convert 14.02 Liters into gallons (3.785L/1.000 Gal). 14.02 L x 1.000 Gal/3.785 L = 3.704095 Gal Again reduced to 4 digits so… 3.704 Gal 6 Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty in the last digit reported. Link to exercise 7 Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements of the same quantity. 8 Significant Figures - Overview 1. 2. 3. Nonzero integers Zeros leading zeros captive zeros trailing zeros Exact numbers 9 Significant Figures - Details Nonzero integers always count as significant figures. 3456 has 4 sig figs. 10 Significant Figures - Details Zeros Leading zeros do not count as significant figures. 0.0486 has 3 sig figs. 11 Significant Figures - Details Zeros Captive zeros always count as significant figures. 16.07 has 4 sig figs. 12 Significant Figures - Details Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 has 4 sig figs. 13 Significant Figures - Details Zeros Trailing zeros are significant only if the number contains a decimal point. 9300 has ??? 14 Significant Figures - Details Zeros 9300 could be 2, could be 3, could be 4??? It is ambiguous. Therefore, Change it to Scientific Notation 15 Significant Figures - Details Zeros 9300 2 sig figs 9.3 X 103 3 sig figs 9.30 X 103 4 sig figs 9.300 X 103 16 Significant Figures - Details • Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm exactly 17 Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 2.0 = 12.76 13 (2 sig figs) 18 Rules for Significant Figures in Mathematical Operations Addition and Subtraction: # sig figs in the result equals the number of decimal places in the least precise measurement. 6.8 + 11.934 = 18.734 18.7 (3 sig figs) 19 Exercise Link Link to exercise 20 Temperature Celsius scale = C Kelvin scale = K Fahrenheit scale = F 21 Temperature Scales • Fahrenheit Scale, °F – Water’s freezing point = 32°F, boiling point = 212°F • Celsius Scale, °C – Temperature unit larger than the Fahrenheit – Water’s freezing point = 0°C, boiling point = 100°C • Kelvin Scale, K – Temperature unit same size as Celsius – Water’s freezing point = 273 K, boiling point = 373 K 22 Temperature 23 Type Unit Conversions What if I want to convert a mass unit into a volume unit? For example, can I convert grams into milliliters? g X --------- = mL g ml/g = mL X grams/milliliter is density 24 Density • Density is the mass of substance per unit volume of the substance: Specific Gravity is the density of a substance relative to the density of water at 4 oC. This has no units! 25