Checklist
Notes
For this unit, we give meaning to large and small numbers.
Use scientific notation to write large and small
numbers.
Put numbers in perspective through estimation...
...perspective through comparison...
...and perspective through scaling.
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Assignment
Notes
Assignment:
1. p 156 Quick Quiz
2. p 157 - 160 Excercises 23, 26, 31, 35, 38, 41, 42, 45,
47, 49, 53, 59, 61, 67
3. p 162 - 167 Read this portion on unit 2C.
4. Quiz over 3A, 3B on February 6.
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Key Words
Notes
Scientific notation - A format to express a number
as a number between 1 and 10 multiplied by a power
of 10.
Order of magnitude - An estimate specifying only a
broad range of values, such as ”in the billions.”
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Scientific Notation
Notes
A number may be rewritten in scientific notation. For
example, one billion is 109 , so six billion is 6 × 109 .
Numbers like 450 are written as 4.5 × 102 and 0.093 is
9.3 × 10−2 . The format writes a number as a number
between 1 and 10 multiplied by a power of 10.
Write each in scientific notation:
Example: The budget total in receipts for 2012 is
$2,450,000,000,000 (whitehouse.gov).
Example: The diameter of a hydrogen nucleus is about
0.000000000000001 meter.
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Approximations
Notes
You estimate that, on average, each of the 8 million
people in a city produces 1.8 pounds of garbage each day.
Estimate the total amount (in tons) of garbage, using 1.8
pounds equals 0.0009 tons.
Is an answer of 225 tons reasonable?
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Estimation
Notes
Estimates are useful even if we only estimate within a
broad range of an exact value. For instance, knowing a
town of city has population in tens of thousands or in the
millions can infer a lot about the characteristics.
Example: Make an order of magnitude estimate of total
annual spending of ice cream in (1) the Salt Lake City
area, and (2) the U.S.
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Comparisons
Notes
How long would it take to count $100 billion in $20 bills?
If one $20 bill is counted per second, then it would take 5
billion seconds. In years, this is about 158.5 years.
Knowing this is useful in dealing with relatively unfamiliar
units (such as energy units).
Example: Compare the U.S. population (give a fair
estimate) to the world population (again estimate) and
the U.S. energy consumption (1 × 1020 Joules) to the
world energy consumption (5 × 1020 Joules.)
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Scaling
Notes
You may read maps with mini-rulers where, ”1 inch = 1
mile.” Such scaling help visualize, but others can help in
timelines, etc.
Exercise: A city map states, ”1 mile = 1 inch.” What is
the scale ratio for that map? A scale ratio coverts one
unit in common with the other. The scale ratio doesn’t
have units.
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More examples with scaling
Notes
Example: The distance from the Earth to the Sun is
about 150 million kilometers. Their diameters are about
12,760 kilometers and 1.4 million kilometers, respectively.
Put these numbers in perspective by using a scale model
of the solar system with a 1 to 10 billion scale.
Example: The distance from Earth to the nearest stars
besides the Sun is about 4.3 light-years. Using the same
scale for the model solar system as above, how far are
these stars from the Earth? (1 light-years is about
9.5 × 1012 kilometers.)
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Case study examples
Notes
In many cases we gain more perspective using two or
more techniques together. In the next examples, ask
whether the numbers have more meaning and how else
you might give meaning to the numbers.
Example: How big is a University? The University of Utah
has about 32,400 students. How long will it take to get to
know each student if a person meets for lunch a group of
5 students at a time?
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Case study examples
Notes
Example: What is a billion dollars How many people can
you employ with $1 billion per year?
Example: What is a billion dollars How long would it take
a sports celebrity paid $1 million per year to earn a total
of $1 billion?
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Conclusion of Unit 3B
Notes
When hearing about quantitative values in the news and
such, give these words meaning using different perspective
techniques. Current national issues are more
understandable putting large or small numbers in
perspective. Does it make sense, for instance:
For a book to have 105 words?
To see about 1050 TV commercials?
To live in a 200-foot tall building?
For Americans to spend $1 billion per year on rent and
mortage payments?
Decide which are true and false, and explain your
reasoning.
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