Numbers in the Real World
1 world
108. Percentages
109. Percentage Change
110. Abuse of Percentages
Copyright © 2011 Pearson Education, Inc.
Unit 3B
Putting Numbers
in Perspective
Copyright © 2011 Pearson Education, Inc.
Slide 3-3
3-B
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.
Slide 3-4
3-B
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.
Slide 3-5
Class Notes (2)
Checking answers with approximations
3-B

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.
Slide 3-6
3-B
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?
servings
$1
spending  50

  3  108  people
person  yr serving
1.5  10

 $15 billion per year
1 yr
10
Copyright © 2011 Pearson Education, Inc.
Slide 3-7
3-B
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.
Slide 3-8
3-B
Giving Meaning to Numbers
Perspective through comparisons
Copyright © 2011 Pearson Education, Inc.
Slide 3-9
3-B
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.
Slide 3-10
Class Notes (5)
Fusion Power


3-B
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.
Slide 3-11
3-B
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.
Slide 3-12
3-B
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.
Slide 3-13
3-B
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.
Slide 3-14
3-B
Class Notes (9)
Timeline

9. Make a simple scale drawing of this timeline
using the football field analogy.
Copyright © 2011 Pearson Education, Inc.
Slide 3-15
Class Notes (10)
Case Studies
3-B

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.
Slide 3-16
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.
3-B
Slide 3-17
3B Homework
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
3-B
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
Slide 3-18