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Standards for Measurement

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  1. Standards for Measurement

  2. Mass and Weight

  3. Mass : The quantity or amount of matter that an object possesses. • Fixed • Independent of the object’s location • Weight: A measure of the earth’s gravitational attraction for an object. • Not fixed • Depends on the object’s location. • Matter: Anything that has mass and occupies space.

  4. Measurement and Significant Figures

  5. Measurements • Experiments are performed. • Numerical values or data are obtained from these measurements.

  6. numerical value 70 kilograms = 154 pounds unit Form of a Measurement

  7. known estimated Significant Figures • The number of digits that are known plus one estimated digit are considered significant in a measured quantity 5.16143

  8. known estimated Significant Figures • The number of digits that are known plus one estimated digit are considered significant in a measured quantity 6.06320

  9. Significant Figures on Reading a Thermometer

  10. The temperature 21.2oC is expressed to 3 significant figures. Temperature is estimated to be 21.2oC. The last 2 is uncertain.

  11. The temperature 22.0oC is expressed to 3 significant figures. Temperature is estimated to be 22.0oC. The last 0 is uncertain.

  12. Significant Figures All nonzero numbers are significant. 461

  13. Significant Figures All nonzero numbers are significant. 461

  14. Significant Figures All nonzero numbers are significant. 461

  15. Significant Figures All nonzero numbers are significant. 3 Significant Figures 461

  16. Significant Figures A zero is significant when it is between nonzero digits. 3 Significant Figures 401

  17. Significant Figures A zero is significant when it is between nonzero digits. 5 Significant Figures 9 3 . 0 0 6

  18. Significant Figures A zero is significant when it is between nonzero digits. 3 Significant Figures 9 . 0 3

  19. Significant Figures A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 5 5 . 0 0 0

  20. Significant Figures A zero is significant at the end of a number that includes a decimal point. 5 Significant Figures 2 . 1 9 3 0

  21. Significant Figures A zero is not significant when it is before the first nonzero digit. 1 Significant Figure 0 . 0 0 6

  22. Significant Figures A zero is not significant when it is before the first nonzero digit. 3 Significant Figures 0 . 7 0 9

  23. Significant Figures A zero is not significant when it is at the end of a number without a decimal point. 1 Significant Figure 5 0 0 0 0

  24. Significant Figures A zero is not significant when it is at the end of a number without a decimal point. 4 Significant Figures 6 8 7 1 0

  25. Scientific Notation of Numbers

  26. Very large and very small numbers are often encountered in science. 602200000000000000000000 0.00000000000000000000625 • Very large and very small numbers like these are awkward and difficult to work with.

  27. 6.25 x 10-21 A method for representing these numbers in a simpler form is scientific notation. 6.022 x 1023 602200000000000000000000 0.00000000000000000000625

  28. Scientific Notation • Write a number as a power of 10 • Move the decimal point in the original number so that it is located after the first nonzero digit. • Follow the new number by a multiplication sign and 10 with an exponent (power). • The exponent is equal to the number of places that the decimal point was shifted.

  29. Write 6419 in scientific notation. decimal after first nonzero digit power of 10 6.419 x 103 64.19x102 641.9x101 6419. 6419

  30. Write 0.000654 in scientific notation. decimal after first nonzero digit power of 10 6.54 x 10-4 0.000654 0.00654 x 10-1 0.0654 x 10-2 0.654 x 10-3

  31. Significant Figures in Calculations

  32. The Metric System

  33. The metric or International System (SI, Systeme International) is a decimal system of units. • It is built around standard units. • It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.

  34. International System’s Standard Units of Measurement Length meter m Quantity Name of Unit Abbreviation Mass kilogram kg Temperature Kelvin K Time second s Amount of substance mole mol Electric Current ampere A Luminous Intensity candela cd

  35. Power of 10 Prefix Symbol Numerical Value Equivalent Prefixes and Numerical Values for SI Units exa E 1,000,000,000,000,000,000 1018 peta P 1,000,000,000,000,000 1015 tera T 1,000,000,000,000 1012 giga G 1,000,000,000 109 mega M 1,000,000 106 kilo k 1,000 103 hecto h 100 102 deca da 10 101 — —1 100

  36. Power of 10 Prefix Symbol Numerical Value Equivalent Prefixes and Numerical Values for SI Units deci d 0.1 10-1 centi c 0.01 10-2 milli m 0.001 10-3 micro 0.000001 10-6 nano n 0.000000001 10-9 pico p 0.000000000001 10-12 femto f 0.00000000000001 10-15 atto a 0.000000000000000001 10-18

  37. Problem Solving

  38. Dimensional Analysis Dimensional analysis converts one unit to another by using conversion factors. unit1 x conversion factor = unit2

  39. Basic Steps • Read the problem carefully. Determine what is to be solved for and write it down. • Tabulate the data given in the problem. • Label all factors and measurements with the proper units.

  40. Basic Steps • Determine which principles are involved and which unit relationships are needed to solve the problem. • You may need to refer to tables for needed data. • Set up the problem in a neat, organized and logical fashion. • Make sure unwanted units cancel. • Use sample problems in the text as guides for setting up the problem.

  41. Basic Steps • Proceed with the necessary mathematical operations. • Make certain that your answer contains the proper number of significant figures. • Check the answer to make sure it is reasonable.

  42. Degree Symbols degrees Celsius = oC Kelvin (absolute) = K degrees Fahrenheit = oF

  43. Temperature Conversions

  44. To convert between the scales use the following relationships.

  45. It is not uncommon for temperatures in the Canadian planes to reach –60oF and below during the winter. What is this temperature in oC and K?

  46. It is not uncommon for temperatures in the Canadian planes to reach –60oF and below during the winter. What is this temperature in oC and K?

  47. Density

  48. Density is the ratio of the mass of a substance to the volume occupied by that substance.

  49. The density of gases is expressed in grams per liter. Mass is usually expressed in grams and volume in ml or cm3.

  50. Density varies with temperature