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. Significant Figures
All nonzero numbers are significant.
461

9. Significant Figures
All nonzero numbers are significant.
461

10. 461 Significant Figures All nonzero numbers are significant.

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

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

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

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

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

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

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

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

19. 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

20. Rounding off Numbers

21. 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.

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.
4 or less
80.873

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.
4 or less

24. 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
drop these figures
increase by 1 6

25. Scientific Notation of Numbers

26. 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.

27. 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.

28. 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

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

30. Significant Figures in Calculations

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

32. Multiplication or Division

33. 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.

34. The correct answer is 440 or 4.4 x 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 x 102

35. Addition or Subtraction

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

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

38. 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
Correct answer.
Round off to the nearest unit.
306.37

39. 0.018286814 Answer given by calculator. Two significant figures.
Drop these 6 digits.
Correct answer.
The answer should have two significant figures because is the number with the fewest significant figures.

40. The Metric System

41. 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.

42. 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)

43. 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

44. 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

45. Problem Solving

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

47. 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.

48. 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.

49. 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.

50. Measurement of Length

51. 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.

52. 1 meter = inches
1 meter is a little longer than a yard

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

55. The conversion factor takes a fractional form.

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

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

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

59. 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

60. Measurement of Mass

61. 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

62. Metric Units of mass Exponential
Unit Abbreviation Gram Equivalent Equivalent
kilogram kg 1,000 g 103 g
gram g 1 g 100 g
decigram dg 0.1 g 10-1 g
centigram cg 0.01 g 10-2 g
milligram mg g 10-3 g
microgram g g 10-6 g

63. Convert 45 decigrams to grams.
1 g = 10 dg

64. Measurement of Volume

65. 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

67. Measurement of Temperature

68. 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.

69. 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.

70. 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.

71. Gabriel Daniel Fahrenheit
Anders Celsius
William Thomson

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

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

74. 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? –

75. 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?

76. Density

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

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

80. Examples

81. 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?

82. 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

83. 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.

84. 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

85. (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.

86. 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

87. The End