1. 1 Chapter 2 - Measurements Section 2.1 Units of Measurement

2. 2 Stating a Measurement In a measurement, a number is followed by a unit. Observe the following examples of measurements: Number Unit 35 m 0.25 L 225 lb 3.4 hr

3. 3 The Metric System (SI) The metric system or SI (international system) is A decimal system based on 10. Used in most of the world. Used everywhere by scientists.

4. 4 Units in the Metric System In the metric (SI) system, one unit is used for each type of measurement: MeasurementMetricSI lengthmeter (m)meter (m) volumeliter (L)cubic meter (m 3 ) massgram (g)kilogram (kg) timesecond (s)second (s) temperatureCelsius (  C)Kelvin (K)

5. 5 Length Measurement Length Is measured using a meter stick. Has the unit of meter (m) in the metric (SI) system.

6. 6 Volume Measurement Volume Is the space occupied by a substance. Has the unit liter (L) in metric system. 1 L = 1.057 qt Uses the unit m 3 (cubic meter) in the SI system. Is measured using a graduated cylinder.

7. 7 Mass Measurement The mass of an object Is the quantity of material it contains. Is measured on a balance. Has the unit gram(g) in the metric system. Has the unit kilogram(kg) in the SI system.

8. 8 Temperature Measurement The temperature of a substance Indicates how hot or cold it is. Is measured on the Celsius (  C) scale in the metric system. In the SI system uses the Kelvin(K) scale.

9. 9 Time Measurement Time measurement Has the unit second(s) in both the metric and SI systems. Is based on an atomic clock that uses a frequency emitted by cesium atoms.

10. 10 Chapter 2 - Measurements Section 2.2 Scientific Notation

11. 11 Scientific Notation Scientific notation Is used to write very large or very small numbers. For the width of a human hair of 0.000 008 m is written as 8 x 10 -6 m For a large number such as 2 500 000 s is written as 2.5 x 10 6 s

12. 12 Scientific Notation A number written in scientific notation contains a coefficient and a power of 10. coefficient power of ten coefficient power of ten 1.5 x 10 2 7.35 x 10 -4 To write a number in scientific notation, the decimal point is moved after the first digit. The spaces moved are shown as a power of ten. 52 000. = 5.2 x 10 4 0.00378 = 3.78 x 10 -3 4 spaces left 3 spaces right

13. 13 Comparing Numbers in Standard and Scientific Notation Number in Standard Format Scientific Notation Diameter of the Earth 12 800 000 m1.28 x 10 7 m Mass of a human 68 kg 6.8 x 10 1 kg Mass of a hummingbird 0.002 kg2 x 10 -3 kg Length of a pox virus 0.000 000 3 cm3 x 10 -7 cm

14. 14 Learning Check Write each number using the correct scientific notation for each. A. 0.000 008 B. 72 000

15. 15 Learning Check Write each as a standard number. A. 2.0 x 10 -2 B. 1.8 x 10 5

16. 16 Section 2.3 Measured Numbers and Significant Figures Chapter 2 - Measurements

17. 17 Measured Numbers A measuring tool Is used to determine a quantity such as height or the mass of an object. Provides numbers for a measurement called measured numbers.

18. 18. l 2.... l.... l 3.... l.... l 4.. cm The markings on the meter stick at the end of the orange line are read as The first digit 2 plus the second digit 2.7 The last digit is obtained by estimating. The end of the line might be estimated between 2.7–2.8 as half-way (0.5) or a little more (0.6), which gives a reported length of 2.75 cm or 2.76 cm. Reading a Meter Stick

19. 19 Known + Estimated Digits In the length reported as 2.76 cm, The digits 2 and 7 are certain (known) The final digit 6 was estimated (uncertain) All three digits (2.76) are significant including the estimated digit

20. 20 Significant Figures in Measured Numbers Significant figures Obtained from a measurement include all of the known digits plus the estimated digit. Reported in a measurement depend on the measuring tool.

21. 21 Significant Figures

22. 22 All non-zero numbers in a measured number are significant. MeasurementNumber of Significant Figures 38.15 cm4 5.6 ft2 65.6 lb3 122.55 m5 Counting Significant Figures

23. 23 Sandwiched zeros Occur between nonzero numbers. Are significant. MeasurementNumber of Significant Figures 50.8 mm3 2001 min4 0.0702 lb3 0.40505 m 5 Sandwiched Zeros

24. 24 Trailing zeros Follow non-zero numbers in numbers without decimal points. Are usually place holders. Are not significant. MeasurementNumber of Significant Figures 25 000 cm 2 200 kg1 48 600 mL3 25 005 000 g 5 Trailing Zeros

25. 25 Leading zeros Precede non-zero digits in a decimal number. Are not significant. Measurement Number of Significant Figures 0.008 mm1 0.0156 oz3 0.0042 lb2 0.000262 mL 3 Leading Zeros

26. 26 Significant Figures in Scientific Notation In scientific notation All digits including zeros in the coefficient are significant. Scientific NotationNumber of Significant Figures 8 x 10 4 m1 8.0 x 10 4 m2 8.00 x 10 4 m3

27. 27 State the number of significant figures in each of the following measurements: A. 0.030 m B. 4.050 L C. 0.0008 g D. 2.80 m Learning Check

28. 28 A. Which answer(s) contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4.76 x 10 3 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 10 3 C. The number of significant figures in 5.80 x 10 2 is 1) one3) two3) three Learning Check

29. 29 In which set(s) do both numbers contain the same number of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150 000 Learning Check

30. 30 Examples of Exact Numbers An exact number is obtained When objects are counted. Counting objects 2 soccer balls 4 pizzas From numbers in a defined relationship. Defined relationships 1 foot = 12 inches 1 meter = 100 cm

31. 31 Exact Numbers

32. 32 Learning Check Classify each of the following as (1) exact or (2) measured numbers. A.__Gold melts at 1064°C. B.__1 yard = 3 feet C.__The diameter of a red blood cell is 6 x 10 -4 cm. D.__There are 6 hats on the shelf. E.__A can of soda contains 355 mL of soda.

33. 33 Chapter 2 - Measurements Section 2.4 Significant Figures in Calculations

34. 34 Rounding Off Answers Often, the correct answer Requires that a calculated answer be rounded off. Uses rounding rules to obtain the correct answer with the proper number of significant figures.

35. 35 Rounding Off Calculated Answers When the first digit dropped is 4 or less, The retained numbers remain the same. 45.832 rounded to 3 significant figures drops the digits 32 = 45.8 When the first digit dropped is 5 or greater, The last retained digit is increased by 1. 2.4884 rounded to 2 significant figures drops the digits 884 = 2.5 (increase by 0.1)

36. 36 Adding Significant Zeros Occasionally, a calculated answer requires more significant digits. Then one or more zeros are added. CalculatedZeros added to answergive 3 significant figures 44.00 1.51.50 0.20.200 12 12.0

37. 37 Learning Check Adjust the following calculated answers to give answers with three significant figures: A. 824.75 cm B. 0.112486 g C. 8.2 L

38. 38 Calculations with Measured Numbers In calculations with measured numbers: Significant figures are counted or place values are determined to give the correct number of figures in the final answer.

39. 39 When multiplying or dividing The answer has the same number of significant figures as in the measurement with the fewest significant figures. Rounding rules are used to obtain the correct number of significant figures. Example: 110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SF Multiplication and Division

40. 40 Give an answer for each with the correct number of significant figures: A. 2.19 x 4.2 = B. 4.311 ÷ 0.07 = C. 2.54 x 0.0028 = 0.0105 x 0.060 Learning Check

41. 41 When adding or subtracting use The same number of digits as the measurement whose last digit has the highest place value. Use rounding rules to adjust the number of digits in the answer. 25.2 one decimal place + 1.34 two decimal places 26.54calculated answer 26.5 answer with one decimal place Addition and Subtraction

42. 42 For each calculation, round the answer to give the correct number of digits. A. 235.05 + 19.6 + 2 = B. 58.925 - 18.2= Learning Check

43. 43 Chapter 2 - Measurements Section 2.5 Prefixes and Equalities

44. 44 Prefixes A prefix In front of a unit increases or decreases the size of that unit. Make units larger or smaller than the initial unit by one or more factors of 10. Indicates a numerical value. prefix=value 1 kilometer=1000 meters 1 kilogram=1000 grams

45. 45 Metric and SI Prefixes

46. 46 Indicate the unit that matches the description: 1. A mass that is 1000 times greater than 1 gram. 2. A length that is 1/100 of 1 meter. 3. A unit of time that is 1/1000 of a second. Learning Check

47. 47 An equality States the same measurement in two different units. Can be written using the relationships between two metric units. Example: 1 meter is the same as 100 cm and 1000 mm. 1 m =100 cm 1 m =1000 mm 100 cm = 1000 mm Metric Equalities

48. 48 Metric Equalities for Volume

49. 49 Metric Equalities for Mass Several equalities can be written for mass in the metric (SI) system 1 kg =1000 g 1 g =1000 mg 1 mg = 0.001 g 1 mg =1000 µg

50. 50 Indicate the unit that completes each of the following equalities: A. 1000 m = B. 0.001 g = C. 0.1 s = D. 0.01 m = Learning Check

51. 51 Chapter 2 - Measurements Section 2.6 Writing Conversion Factors

52. 52 Equalities Use two different units to describe the same measured amount. Are written for relationships between units of the metric system, U.S. units or between metric and U.S. units. For example, 1 m = 1000 mm 1 lb = 16 oz 2.205 lb = 1 kg Equalities

53. 53 Exact and Measured Numbers in Equalities Equalities between units of The same system are definitions and use exact numbers. Different systems (metric and U.S.) use measured numbers and count as significant figures.

54. 54 Some Common Equalities

55. 55 A conversion factor Is a fraction obtained from an equality. Equality: 1 in. = 2.54 cm Is written as a ratio with a numerator and denominator. Can be inverted to give two conversion factors for every equality. 1 in. and 2.54 cm 2.54 cm 1 in. Conversion Factors

56. 56 Write conversion factors for each pair of units: A. liters and mL B. hours and minutes C. meters and kilometers Learning Check

57. 57 Factors with Powers A conversion factor Can be squared or cubed on both sides of the equality. Equality1 in. = 2.54 cm 1 in. and 2.54 cm 2.54 cm 1 in. Squared(1 in.) 2 = (2.54 cm) 2 (1 in.) 2 and (2.54 cm) 2 (2.54 cm) 2 (1 in.) 2 Cubed (1 in.) 3 = (2.54 cm) 3 (1 in.) 3 and (2.54 cm) 3 (2.54 cm) 3 (1 in.) 3

58. 58 A conversion factor May be obtained from information in a word problem. Is written for that problem only. Example: The price of one pound (1 lb) of red peppers is $2.39. 1 lb red peppers and$2.39 $2.391 lb red peppers Conversion Factors in a Problem

59. 59 Chapter 2 - Measurements Section 2.7 Problem Solving

60. 60 To solve a problem Identify the given unit. Identify the needed unit. Problem: A person has a height of 2.0 meters. What is that height in inches? The given unit is the initial unit of height. given unit = meters (m) The needed unit is the unit for the answer. needed unit = inches (in.) Given and Needed Units

61. 61 Setting up a Problem How many minutes are 2.5 hours? given unit= needed unit= plan=

62. 62 A rattlesnake is 2.44 m long. How long is the snake in centimeters? Learning Check

63. 63 Often, two or more conversion factors are required to obtain the unit needed for the answer. Unit 1 Unit 2 Unit 3 Additional conversion factors can be placed in the setup to cancel each preceding unit Given unit x factor 1 x factor 2 = needed unit Unit 1 x Unit 2 x Unit 3 = Unit 3 Unit 1 Unit 2 Using Two or More Factors

64. 64 How many minutes are in 1.4 days? Example: Problem Solving

65. 65 Be sure to check your unit cancellation in the setup. The units in the conversion factors must cancel to give the correct unit for the answer. What is wrong with the following setup? 1.4 day x 1 day x 1 hr 24 hr 60 min Units = day 2 /min is Not the needed unit Units don’t cancel properly. Check the Unit Cancellation

66. 66 Learning Check What is 165 lb in kg?

67. 67 A bucket contains 4.65 L water. How many gallons of water is that? Learning Check

68. 68 If a ski pole is 3.0 feet in length, how long is the ski pole in mm? Learning Check

69. 69 If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet? Learning Check

70. 70 Section 2.8 Density Chapter 2 - Measurements

71. 71 Density Compares the mass of an object to its volume. Is the mass of a substance divided by its volume. Note: 1 mL = 1 cm 3 Is expressed as D = mass = g or g = g/cm 3 volume mL cm 3 Density

72. 72 Densities of Common Substances

73. 73 Osmium is a very dense metal. What is its density In g/cm 3 if 50.0 g of osmium has a volume of 2.22 cm 3 ? Learning Check

74. 74 Volume by Displacement A solid completely submerged in water displaces its own volume of water. The volume of the solid is calculated from the volume difference. 45.0 mL - 35.5 mL = 9.5 mL = 9.5 cm 3

75. 75 What is the density (g/cm 3 ) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added? 25.0 mL 33.0 mL object Learning Check

76. 76 Sink or Float Ice floats in water because the density of ice is less than the density of water. Aluminum sinks because its density is greater than the density of water.

77. 77 Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) 1 2 3 K K W W W V V V K Learning Check

78. 78 Density can be written as an equality. For a density of 3.8 g/mL, the equality is: 3.8 g = 1 mL From this equality, two conversion factors can be written: Conversion 3.8 g and 1 mL factors1 mL 3.8 g Density as a Conversion Factor

79. 79 The density of octane, a component of gasoline, is 0.702 g/mL. What is the mass, in kg, of 875 mL of octane? Learning Check

80. 80 If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil? Learning Check

81. 81 A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 lb aluminum, how many liters of aluminum (D=2.70 g/cm 3 ) are obtained from the cans? Learning Check

82. 82 Which of the following samples of metals will displace the greatest volume of water? 1 2 3 25 g of aluminum 2.70 g/mL 45 g of gold 19.3 g/mL 75 g of lead 11.3 g/mL Learning Check