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MATH 150 – G
03/04/2009
PUTTING NUMBERS IN PERSPECTIVE
Scientific Notation:
A number can be expressed as a number between 1 and 10 multiplied by a power of 10.
1 billion = 109
1 trillion = 1012
0.56 = 5.6 x 10-1
450 = 4.5 x 102
a) Converting to scientific notation
2044=
0.0023 =
65 x 103 =
b) Converting from scientific notation
3.22 x 103 =
1.02 x 105 =
9.3 x 10-2 =
c) Multiplication and division
(6 "10 2 ) " (5 "10 4 ) =
2.3 "10#3
=
4.6 "10#4
d) Addition and subtraction:
(3 "10 4 ) + (5 "10 2 ) =
Writing Large and Small numbers:
Example 1: Write the following in scientific notation
a) The U.S. federal debt is about $10,900,000,000,000
b) B) The diameter of a hydrogen nucleus is about 0.000000000000001
Approximations with Scientific Notation:
Example 2: We can approximate quickly the answer to 6956 x 413
Giving Meaning to the numbers:
a) Perspective through estimation
Example 3: How high is 100 feet?
An order of magnitude estimate specifies only a broad range of values, such as “in the ten thousands” or
“in the millions.”
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Example 4: The population of U.S. is “on the order of 300 million”
Number of stars in the galaxy is “of the order 100 billion”
Example 5: Could a person walk across the United States (New York to California) in a year? If not, about
how long would it take?
b) Perspective through comparisons
Example 6: How much money is 1 trillion of dollars?
c) Perspective through scaling
There are three ways of expressing scales:
Verbally: “One centimeter represents one kilometer”
Graphically: A marked miniruler can show the scale visually (usually maps, atlas – see textbook for an
example)
Ratio: We can state the ratio of a scale size to an actual size.
Example 7: Represent “One centimeter represents one kilometer” as a ratio
Example 8: A city map states, “One inch represents one mile.” What is the scale ratio?
Putting It All Together:
Example 9: How big is a university? Suppose that a large university has 25,000 students. Imagine that the
new university president wants to get to know the students. She proposes to meet for lunch with groups of
5 students at a time. Is it possible for her to have lunch with all the students? Consider that she holds the
lunch meetings five days per week and she has lunches 50 weeks per year.
Homework: Check examples of section 3B of the textbook and do the following exercises
Page 168 – exercises 25 (a,c,e), 26 (a,c,d,e), 27 (a, c, e, f), 29 (a, c, d), 41, 43, 61, 63.
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