1. Standards for Measurement Chapter 2
Larry Emme
Chemeketa Community College

2. Measurement and Significant Figures

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

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

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

6. Exact Numbers
Exact numbers have an infinite numbers of significant figures.
Exact numbers occur in simple counting operations 2 1 3 5 4
Defined numbers are exact.
100 centimeters = 1 meter
12 inches = 1 foot

7. Significant Figures
All nonzero numbers are significant.
461

8. 461 Significant Figures All nonzero numbers are significant.

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

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

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

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

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

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

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

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

17. 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

18. Rounding off Numbers

19. Rounding Off Numbers
Often when calculations are performed extra digits are present in the results.
It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures.
When digits are dropped the value of the last digit retained is determined by a process known as rounding off numbers.

20. Rounding Off Numbers
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
80.873

21. Rounding Off Numbers
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
4 or less
80.873

22. Rounding Off Numbers
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
80.87

23. Rounding Off Numbers
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.

24. Rounding Off Numbers
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
4 or less

25. Rounding Off Numbers
Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.
1.875

26. Rounding Off Numbers
Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1.

27. Rounding Off Numbers
Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1.
5 or greater
increase by 1

28. Rounding Off Numbers
Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1.
drop these figures

29. Rounding Off Numbers
Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1.
5.46

30. Scientific Notation of Numbers

31. If a number is larger than 1
Scientific notation
If a number is larger than 1
Move decimal point X places left to get a number between 1 and 10.
, ,
= x 108
The resulting number is multiplied by 10X.

32. Scientific notation 0. 0 0 0 0 0 0 1 2 3 = 1.23 x 10-7
If a number is smaller than 1
Move decimal point X places right to get a number between 1 and 10.
= x 10-7
The resulting number is multiplied by 10-X.

33. Examples
Write in Scientific Notation:
25 = = = =
3,210. =
2.5 x 101
x 103
5.93 x 10-4
4 x 10-7
3.210 x 103

34. Scientific notation 1.44939 × 10-2 = 0.0144939 On Calculator
(-) 2
×10 EE
Means
×10
Change
Sign

35. Significant Figures in Calculations

36. The results of a calculation cannot be more precise than the least precise measurement.

37. Multiplication or Division

38. 6.581 feet
29 feet ?
Area = Sq Ft

39. 6.581 feet
29 feet
Area = Sq Ft
Area = 190 Sq Ft

40. In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

41. The correct answer is 440 or 4.4 × 102
2.3 has two significant figures.
(190.6)(2.3) =
190.6 has four significant figures.
Answer given by calculator.
The answer should have two significant figures because 2.3 is the number with the fewest significant figures.
Drop these three digits.
Round off this digit to four.
438.38
The correct answer is 440 or 4.4 × 102

42. Addition or Subtraction

43. The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.

44. The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

45. Round off to the nearest unit.
Add , 129 and 52.2
Least precise number.
125.17
129.
52.2
Answer given by calculator.
306.37
Round off to the nearest unit.
Correct answer.
306

46. 0.018 answer Answer given by calculator. Two significant figures.
Drop these 6 digits.
The answer should have two significant figures because is the number with the fewest significant figures.
0.018 answer

47. The Metric System

48. 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.

49. Standard Units of Measurement
Quantity Metric Unit (abbr.) SI Unit (abbr.)
Length meter (m) meter (m)
Mass gram (g) kilogram (kg)
Volume liter (L) cubic meter (m3)
Temperature Celsius (ºC) Kelvin (K)
Energy calorie (cal) Joule (J)
Pressure atmosphere (atm) pascal (Pa)

50. Prefixes and Numerical Values for SI Units
Power of 10
Prefix Symbol Numerical Value Equivalent
exa E 1,000,000,000,000,000,
peta P 1,000,000,000,000,
tera T 1,000,000,000,
giga G 1,000,000,
mega M 1,000,
kilo k 1,
hecto h
deca da
— — 1 100

51. Prefixes and Numerical Values for SI Units
Power of 10
Prefix Symbol Numerical Value Equivalent
deci d
centi c
milli m
micro 
nano n
pico p
femto f
atto a

52. Measurement of Length

53. Metric Units of Length Exponential
Unit Abbreviation Metric Equivalent Equivalent
kilometer km 1,000 m 103 m
meter m 1 m 100 m
decimeter dm 0.1 m 10-1 m
centimeter cm 0.01 m 10-2 m
millimeter mm m 10-3 m
micrometer m m 10-6 m
nanometer nm m 10-9 m
angstrom Å m m

54. The standard unit of length in the SI system is the meter
The standard unit of length in the SI system is the meter. 1 meter is the distance that light travels in a vacuum during
of a second.

55. 1 meter = inches
1 meter is a little longer than a yard

56. Problem Solving

57. Dimensional Analysis Unit Analysis Factor Label Method Using Conversion Factors

58. Problem Solving Using Conversion Factors
Many problems require a change of one number or variable to another by using fractions. 3
The answer “3” must appear on the top of the fraction
The “4” is cross-cancelled by placing it on the bottom of the fraction

59. Problem Solving Using Conversion Factors
Find the conversion factor for the following. 2 9
The answer “2” must appear on the top of the fraction
The “9” is cross-cancelled by placing it on the bottom of the fraction

60. Problem Solving Using Conversion Factors
Find the conversion factor for the following. 5 6
The answer “6” must appear on the bottom of the fraction
The “5” is cross-cancelled by placing it on the top of the fraction

61. Problem Solving Using Conversion Factors
Find the conversion factor for the following. 5 6
The answer “6” must appear on the bottom of the fraction
The “5” is cross-cancelled by placing it on the top of the fraction

62. Problem Solving Using Conversion Factors
Find the conversion factor for the following. b a
The answer “b” must appear on the top of the fraction
The “a” is cross-cancelled by placing it on the bottom of the fraction

63. Problem Solving Using Conversion Factors
Units may be changed in a similar way as numbers and variables.
feet
inches
The answer “feet” must appear on the top of the fraction
The “inches” is cross-cancelled by placing it on the bottom of the fraction

64. Problem Solving Using Conversion Factors summary
Problems containing units require a change of one unit to another unit by using fractions (conversion factors).
1st unit × conversion factor = 2nd unit

65. How many feet are there in 22.5 inches?
1st unit × conversion factor = 2nd unit
in × conversion factor = ft

66. How many feet are there in 22.5 inches?
The conversion factor must accomplish two things:
unit1 x conversion factor = unit2
in × conversion factor = ft
It must cancel inches.
It must introduce feet

67. The conversion factor takes a fractional form.

68. Putting in the measured value and the ratio of feet to inches produces:

69. Convert 3.7×1015 in to miles.
Inches can be converted to miles by writing down conversion factors in succession.
in  ft  miles

70. Convert 3.7×1015 in to miles.
Inches can be converted to miles by writing down conversion factors in succession.
in  ft  miles

71. Convert 4.51030 cm to kilometers.
Centimeters can be converted to kilometers by writing down conversion factors in succession.
cm  m  km

72. Convert 4.51030 cm to kilometers.
Centimeters can be converted to kilometers by writing down conversion factors in succession.
cm  m  km

73. Conversion of units Examples: 10.7 T = ? fl oz 62.04 mi = ? in
5.5 kg = ? mg
9.3 ft = ? cm
5.7 g/ml = ? lbs/qt
3.18 in2 = ? cm2

74. Conversion of units Examples: 10.7 T = ? fl oz 62.04 mi = ? in
5.5 kg = ? mg
9.3 ft = ? cm
5.7 g/ml = ? lbs/qt
3.18 in2 = ? cm2

75. Measurement of Mass

76. The standard unit of mass in the SI system is the kilogram
The standard unit of mass in the SI system is the kilogram. 1 kilogram is equal to the mass of a platinum-iridium cylinder kept in a vault at Sevres, France.
1 kg = pounds

77. Measurement of Volume

78. Volume is the amount of space occupied by matter.
In the SI system the standard unit of volume is the cubic meter (m3).
The liter (L) and milliliter (mL) are the standard units of volume used in most chemical laboratories. 1 mL = 1 cm3 = 1cc

80. Measurement of Temperature

81. Heat
A form of energy that is associated with the motion of small particles of matter.
Heat refers to the quantity of this energy associated with the system.
System is the entity that is being heated or cooled.

82. Temperature A measure of the intensity of heat.
It does not depend on the size of the system.
Heat always flows from a region of higher temperature to a region of colder temperature.

83. Temperature Measurement
The SI unit of temperature is the Kelvin.
There are three temperature scales: Kelvin, Celsius and Fahrenheit.
In the laboratory temperature is commonly measured with a thermometer.

84. Gabriel Daniel Fahrenheit
Anders Celsius
William Thomson

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

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

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

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

89. Density

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

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

92. Densities of Some Selected Materials
Liquids & Solids
Gases
Substance
Density (g/ml)
Density (g/L)
Wood
0.512
Hydrogen
0.090
Ethyl Alcohol
0.789
Helium
0.178
Vegetable Oil
0.91
Methane
0.714
Water (4°C)
1.0000
Ammonia
0.771
Sugar
1.59
Neon
0.90
Glycerin
1.26
Carbon Monoxide
1.25
Magnesium
1.74
Nitrogen
1.251
Sulfuric Acid
1.84
Air
1.293
Sulfur
2.07
Oxygen
1.429
Salt
2.16
Hydrogen Chloride
1.63
Silver
10.5
Argon
1.78
Lead
11.34
Carbon Dioxide
1.963
Mercury
13.55
Chlorine
3.17
Gold
19.3

93. Examples

94. A 13. 5 mL sample of an unknown liquid has a mass of 12. 4 g
A 13.5 mL sample of an unknown liquid has a mass of 12.4 g. What is the density of the liquid?

95. A graduated cylinder is filled to the 35. 0 mL mark with water
A graduated cylinder is filled to the 35.0 mL mark with water. A copper nugget weighing 98.1 grams is immersed into the cylinder and the water level rises to the 46.0 mL. What is the volume of the copper nugget? What is the density of copper?
35.0 mL
46.0 mL
98.1 g

96. A graduated cylinder is filled to the 35. 0 mL mark with water
A graduated cylinder is filled to the 35.0 mL mark with water. A copper nugget weighing 98.1 grams is immersed into the cylinder and the water level rises to the 46.0 mL. What is the volume of the copper nugget? What is the density of copper?
35.0 mL
46.0 mL
98.1 g

97. The density of ether is 0. 714 g/mL. What is the mass of 25
The density of ether is g/mL. What is the mass of 25.0 milliliters of ether?
Method 1
(a) Solve the density equation for mass.
(b) Substitute the data and calculate.

98. The density of ether is 0. 714 g/mL. What is the mass of 25
The density of ether is g/mL. What is the mass of 25.0 milliliters of ether?
Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:
mL → g
The conversion of units is

99. (b) Substitute the data and calculate.
The density of oxygen at 0oC is g/L. What is the volume of grams of oxygen at this temperature?
Method 1
(a) Solve the density equation for volume.
(b) Substitute the data and calculate.

100. The conversion of units is
The density of oxygen at 0oC is g/L. What is the volume of grams of oxygen at this temperature?
Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:
g → L
The conversion of units is

101. The End