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SI Units SYSTÉME INTERNATIONAL D´UNITÉS Defining the kilogram http://www.youtube.com/watch?v=ZMByI4s-D-Y The need for SI Units At the end of the eighteenth century, science and technology were growing by leaps and bounds across the developed world. New scientific studies needed to be shared between countries and needed to have the same units of measurement in order to be accurately compared In 1791, the metric system was established in Europe In 1875, The Metre Convention was established – a group of international scientists that would get together every 4-6 years to discuss units of measurement The most recent additional was the mole in 1971 Base Units UNITS THAT CANNOT BE DERIVED FROM OTHER UNITS Mass SI Unit: kilogram (kg) Original definition (1793) – The grave was defined as the mass of one cubic decimetre of pure water at its densest point (4° C) Current definition (1889) – The mass of the International Prototype Kilogram or “Big K” The Indus Valley Civilization were the first to develop a system of weights and measures (4000 BC) Length SI Unit: metre (m) Original definition (1793): 1/10,000,000 of the distance between the North Pole and the equator, in a line going through Paris Current definition (1983): The distance traveled by light in a vacuum in 1/299,792,458 seconds The ancient Egyptians (3000 BC) used the unit cubit to measure length – the length from the elbow to the tip of the middle finger. It is believed that yards, feet, and inches were derived from this. Time SI Unit: second (s) Original Definition (Medieval): 1/86,400 day Current Definition (1967): the time it takes to transition between two states of caesium 133 Ancient calendars marked the passage of time as early as 6000 years ago Ancient time keepers include Egyptian sundials, Persian water clocks, and European hourglasses Temperature SI Unit: kelvin (K) Original definition (1743): established the centigrade scale (°C) by assigning 0°C to the freezing point of water and 100°C to the boiling point of water Current definition (1967): assigned 0 K to absolute zero – the point at which all atomic motion stops Amount of a substance SI Unit: mole (mol) Original definition (1900): The molecular weight of a substance in grams Current definition (1967): The amount of substance that contains as many “parts” as 0.012 kg of Carbon12 Avogadro’s number: 6.02 x 1023 molecules per mole Derived units Weight The force on an object due to gravity NOT the same as mass: Weight = mass x gravity SI Unit: newton (N) The ancient Greek had many definitions of weight: Aristotle – weight was the opposite of levity and the two competed to determine if an object would sink or float. The earth had ultimate weight and fire had ultimate levity. Plato described weight as an objects desire to seek out its kin Galileo was the first to determine that weight was related to the mass of an object Speed SI Unit: meter per second (m/s or ms1) Used to describe the time it takes an object to travel a given distance Area SI Unit: square meters (m2) Used to describe the space occupied by a two dimensional object Volume SI Unit: cubic meter (m3) Used to describe the space an object occupies Density SI Unit: kilogram per meter cubed (kg/m3 or kgm-3) Describes how compact a substance is Density = mass/volume Energy SI Unit: Joule (J) Named after James Prescott Joule Energy is the capacity to do work or to produce heat Calorie (cal) is the heat needed to raise 1 gram of water by 1°C 1 cal = 4.18 J Prefixes Larger than the base deca – 101 hecto – 102 kilo – 103 mega – 106 giga – 109 tera – 1012 10 100 1000 1000000 1000000000 1000000000000 Smaller than base deci – 10-1 centi – 10-2 milli – 10-3 micro – 10-6 nano – 10-9 pico – 10-12 0.1 0.01 0.001 0.000001 0.000000001 0.000000000001 Making Measurements HOW TO BE ACCURATE, PRECISE, AND COMPLETE IN YOUR ANSWERS Making Measurements Qualitative – measurements are words, like heavy or hot Quantitative – measurements involve number (quantities) and depend on: The reliability of the measuring instrument The care with which it is read (This depends on YOU!) Scientific Notation Coefficient raised to the power of ten (ex. 1.3 x 107 instead of 13000000) Accuracy, Precision and Error Accuracy – how close a measurement is to the true value Precision – how close the measurements are to each other (reproducibility) Neither accurate nor precise Precise, but not accurate Precise AND accurate Accuracy, Precision, and Error Accepted value – the correct value based on reliable references Experimental value – the value measured in the lab by you Error – accepted value – experimental value Can be positive or negative Percent error – the absolute value of the error divided by the accepted value, then multiplied by 100% Why is there uncertainty? Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places Which of the balances below has the greatest uncertainty in measurement? Significant Figures in Measurements Significant Figures in a measurement include all of the digits that are known, plus one more digit that is estimated Measurements must be reported to the correct number of significant figures Rules for Counting Significant Figures Non-zeros always count as significant figures: 3456 has 4 significant figures Rules for Counting Significant Figures Zeros Leading zeroes do not count as significant figures: 0.0486 has 3 significant figures Rules for Counting Significant Figures Zeros Captive zeroes always count as significant figures: 16.07 has 4 significant figures Rules for Counting Significant Figures Zeros Trailing zeros are significant only if the number contains a written decimal point: 9.300 has 4 significant figures Rules for Counting Significant Figures Two special situations have an unlimited number of significant figures: 1. Counted items a) 23 people, or 425 thumbtacks 2. Exactly defined quantities b) 60 minutes = 1 hour Sig Fig Practice #1 How many significant figures in the following? 1.0070 m 17.10 kg 100,890 L 3.29 x 103 s 0.0054 cm 3,200,000 mL 5 dogs Significant Figures in Calculations In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated. Ever heard that a chain is only as strong as the weakest link? Sometimes, calculated values need to be rounded off. Rounding Calculated Answers Rounding Decide how many significant figures are needed (more on this very soon) Round to that many digits, counting from the left Is the next digit less than 5? Drop it. Next digit 5 or greater? Increase by 1 Rounding Calculated Answers Addition and Subtraction The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem. Rounding Calculated Answers Multiplication and Division Round the answer to the same number of significant figures as the least number of significant figures in the problem. 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 x 2.0 = 12.76 13 (2 sig figs) Sig Fig Practice #2 Calculation Calculator says: 3.24 m x 7.0 m 22.68 m2 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 1.030 g x 2.87 mL 2.9561 g/mL Answer Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places 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) Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 10.24 m 10.2 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL *Note the zero that has been added.