2. Numbers in the Real World
108. Percentages
109. Percentage Change
110. Abuse of Percentages
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3. Putting Numbers in Perspective
Unit 3B
Putting Numbers in Perspective
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4. Scientific Notation
Scientific notation is a format in which a number is expressed as a number between 1 and 10 multiplied by a power of 10.
Examples:
6,700,000,000 in scientific notation is 6.7  109
is 2.0  1015
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5. Class Notes (1) Numbers in Scientific Notation
Rewrite each of the following statements using scientific notation.
Total spending in the new federal budget is 3,500,000,000,000.
The diameter of a hydrogen nucleus is about meter
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6. Class Notes (2) Checking answers with approximations
You and a friend are doing a rough calculation of how much garbage New City residents produce every day. You estimate that, on average, each of the 8 million residents produces 1.8 pounds, or ton, of garbage each day.
8,000,000 persons x ton/person
2. Your friend tells you that the answer is 225 tons. Without using your calculation, determine whether the answer is reasonable.
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7. Giving Meaning to Numbers
Perspective through estimation
An order of magnitude estimate specifies a broad range of values.
Example: Is the total annual ice cream spending in the United States measured in thousands of dollars, millions of dollars, or billions of dollars?
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8. Class Notes (3) Order of Magnitude of Ice Cream Spending
3. Make an order of magnitude estimate of total annual spending on ice cream in the United States.
Total annual spending = serving per person per year x price per serving x population
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9. Giving Meaning to Numbers
Perspective through comparisons
Help students understand the impact that exponents make in scientific notation by discussing the comparisons made in this table.
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10. Class Notes (4) US vs. World Energy Consumption
Compare the US population to the world population and US energy consumption to the world energy consumption.
US pop/world pop
4. What does this tell you about energy usage by Americans?
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11. Class Notes (5) Fusion Power
No one has yet succeeded in creating a commercially viable way to produce energy through nuclear fusion. However, suppose that at some time in the future we are able to build fusion power plants that are safe and cost efficient.
If we could extract all the hydrogen from water and use it for fusion, how much water would we need each minute to meet US energy needs?
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12. Giving Meaning to Numbers
Perspective through scaling
Verbally: “1 cm = 1 km”
Graphically:
As a ratio: 1 cm = 1 km means a scale ratio of 1 to 100,000
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13. Class Notes (6 and 7) Scale Ratio and Earth and Sun
6. A city map states “One inch represents one mile” What is the scale ratio for this map?
7. The distance from the Earth to the Sun is about 150 million kilometers. The diameter of the sun is about 1.4 million kilometers and the diameter of the Earth is about 12,760 kilometers. Put these numbers in perspective by using a scale model of the solar system with a 1 to 10 billion scale.
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14. Class Notes (8) Distance to the Stars (video)
The distance from the Earth to the nearest stars besides the Sun is about 4.3 light years.
8. On the 1 to 10 billions scale, how far are those stars from the Earth?
Note: A light year is the distance that light can travel in one year, 1 light year = 9.5x10^12 km.
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15. Class Notes (9) Timeline
9. Make a simple scale drawing of this timeline using the football field analogy.
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16. Class Notes (10) Case Studies
How big is a university?
10. Tell why it is impossible for the President to meet all 25,000 people by taking 5 to lunch every day.
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17. Class Notes (11-13) Case Studies
11. What is a billion dollars?
12. The Scale of the Atom?
13. Until the Sun Dies
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18. 3B Homework Discussion Paragraph 3A Class Notes 1-11 Quick Quiz 1-10
Exercises p.157:1-14
1 web
74. Energy Comparisons
75. Nuclear Fusion
76. Scale Model Solar System
77. Richest People
1 world
78. Large Numbers
79. Perspective in the News
80. Putting Numbers in Perspective