Numbers in the Real World 108. Percentages 109. Percentage Change 110. Abuse of Percentages Copyright © 2011 Pearson Education, Inc.

Putting Numbers in Perspective Unit 3B Putting Numbers in Perspective Copyright © 2011 Pearson Education, Inc.

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 0.000000000000002 is 2.0  1015 Copyright © 2011 Pearson Education, Inc.

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 .00000000000001 meter Copyright © 2011 Pearson Education, Inc.

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 .0009 ton, of garbage each day. 8,000,000 persons x .0009 ton/person 2. Your friend tells you that the answer is 225 tons. Without using your calculation, determine whether the answer is reasonable. Copyright © 2011 Pearson Education, Inc.

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? Copyright © 2011 Pearson Education, Inc.

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 Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Education, Inc.

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? Copyright © 2011 Pearson Education, Inc.

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? Copyright © 2011 Pearson Education, Inc.

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 Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Educatio, Inc.

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. Copyright © 2011 Pearson Education, Inc.

Class Notes (9) Timeline 9. Make a simple scale drawing of this timeline using the football field analogy. Copyright © 2011 Pearson Education, Inc.

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. Copyright © 2011 Pearson Education, Inc.

Class Notes (11-13) Case Studies 11. What is a billion dollars? 12. The Scale of the Atom? 13. Until the Sun Dies Copyright © 2011 Pearson Education, Inc.

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