SI Units

1. SI Units Systéme International d´unités

2. Defining the kilogram http://www.youtube.com/watch?v=ZMByI4s-D-Y

3. 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

4. Base Units Units that cannot be derived from other units

5. 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)

6. 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.

7. 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

8. 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

9. 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 Carbon-12 Avogadro’s number: 6.02 x 1023 molecules per mole

10. Derived units

11. 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

12. Speed SI Unit: meter per second (m/s or ms-1) Used to describe the time it takes an object to travel a given distance

13. Area SI Unit: square meters (m2) Used to describe the space occupied by a two dimensional object

14. Volume SI Unit: cubic meter (m3) Used to describe the space an object occupies

15. Density SI Unit: kilogram per meter cubed (kg/m3 or kgm-3) Describes how compact a substance is Density = mass/volume

16. 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

17. Prefixes

18. Larger than the base deca – 101 10 hecto – 102 100 kilo – 103 1000 mega – 106 1000000 giga – 109 1000000000 tera – 1012 1000000000000

19. Smaller than base deci – 10-1 0.1 centi – 10-2 0.01 milli – 10-3 0.001 micro – 10-6 0.000001 nano – 10-9 0.000000001 pico – 10-12 0.000000000001

20. Making Measurements How to be accurate, precise, and complete in your answers

21. 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 107instead of 13000000)

22. 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

23. 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%

24. 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?

25. 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

26. Rules for Counting Significant Figures Non-zerosalways count as significant figures: 3456has 4significant figures

27. Rules for Counting Significant Figures Zeros Leading zeroes do not count as significant figures: 0.0486 has 3 significant figures

28. Rules for Counting Significant Figures Zeros Captive zeroes always count as significant figures: 16.07has 4 significant figures

29. 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

30. Rules for Counting Significant Figures Two special situationshave an unlimited number of significant figures: • Counted items • 23 people, or 425 thumbtacks • Exactly defined quantities • 60 minutes = 1 hour

31. 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 

32. 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.

33. 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

34. Rounding Calculated Answers • Addition and Subtraction • The answer should be rounded to the same number of decimal placesas the least number of decimal places in the problem.

35. Rounding Calculated Answers • Multiplication and Division • Round the answer to the same number of significant figuresas the least number of significant figures in the problem.

36. 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)

37. Sig Fig Practice #2 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 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 2.9561 g/mL 1.030 g x 2.87 mL

38. 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)

39. Sig Fig Practice #3 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1821.6 lb 1818.2 lb + 3.37 lb 1821.57 lb 0.160 mL 0.16 mL 2.030 mL - 1.870 mL *Note the zero that has been added.