Measurements and solving problems

2. Measurements and solving problems

3. Standards of measurement

4. SI Units • The 11th General Conference on Weights and Measures (1960) adopted the name Système International d'Unités (International System of Units, international abbreviation SI), for the recommended practical system of units of measurement.

5. Fundamental SI Units (p 32) • Length – meter (m) • Mass – kilogram (kg) • Time – second (s)

6. SI prefixes • kilo (k) - 103, 1000 • centi (c) - 10-2, 1/100 • milli (m) - 10-3, 1/1000 • micro (m) - 10-6, 1/1,000,000 • nano (n) - 10-9, 1/1,000,000,000 • pico (p) - 10-12, 1/1,000,000,000,000

7. examples • 1 millimeter (1 mm) = 0.001 m • 1 nanoliter (1 nL) = 1 x 10-9 L • 1 kilometer (1 km) = 1000 m

8. English - Metric conversions • 1 inch = 2.54 cm • 1 mile = 1.61 km • 1 pound = 0.45 kg • 1 quart = 0.95 L

9. Factor Label method 250 mL = ? L 1000 mL = 1 L 250 mL x 250 mL x 1L 1000 mL = 250 mL x 1L 1000 mL = 0.25 L

10. 2.1 m = ? cm 1 m = 100 cm 2.1 m x 2.1 m x 100 cm 1 m = 2.1 m x 100 cm 1 m = 210 cm

11. Derived SI Units • Volume – liter (L) • Density (mass per unit volume) • g/ cm3 • Density = mass/ volume • d = m/v

12. Density = 10.0 g/ cm3 • Volume = 2.0 cm3 • Mass = ? d = m/v m = d x v = (10.0 g/ cm3) (2.0 cm3) = 20. g

13. Measurement of volume by water displacement Eureka ('Eureka!', or 'Heureka'; Greek ηὕρηκα (later εὕρηκα); is a famous exclamation attributed to Archimedes. He reportedly uttered the word when he suddenly understood that the volume of an irregular object could be calculated by finding the volume of water displaced when the object was submerged in water, subsequently leaping out of his bathtub and running through the streets of Syracuse naked.

14. temperature • Avg. KE of particles in a sample of matter

15. heat • Sum total of KE of particles in a sample of matter

16. Temperature scales • Celsius (oC) • Kelvin (K) • T(K)= t(oC) +273

17. Units of heat • Joule (J) • Calorie (cal) • 1 cal = 4.184 J • E value of food reported in kcal (called calories)

18. accuracy • Closeness of measurement to accepted value

19. precision • Agreement of values

20. Accuracy and precision

21. % error • Value accepted - Value experimental __________________________ x 100% Value accepted

22. Significant figures

23. Significant figures • Measurement of all digits known with certainty + one uncertain final digit

24. How many sig figs? • 33.4 (3) • 1004.1 (5) • 9000000 (1) • 0.0000072 (2) • 82.6000 (6)

25. Sig figs: addition and subtraction • Round off so that final digit is in the same place as leftmost uncertain digit 410.143 32 +________ 442.143 442

26. Sig figs: multiplying and dividing • Round off to the # of digits in the number w/ fewest sig figs 14.00 x2.0 _____ 28.00 28

27. Exact conversion factors DO NOT limit # of digits

28. Scientific notation pp 52-53 • 789,000.0 7.890000 x 105 • 0.000743 7.43 x 10-4

29. Direct proportion (relationship)

30. Inverse proportion (relationship)