MAT 1043
3B Putting Numbers in Perspective
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OBJECTIVES:
1.) Review scientific notation
2.) Perspective through estimation
3.) Perspective through comparisons
EXTRA PRACTICE: UM 11th ed. p. 148 Exercises: 11, 12, 15, 17, 19, 29, 33, 39, 55, 56, 57, 59, 67, 71, 75, 79, 83e
SCIENTIFIC NOTATION:
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:
𝑁 × 10𝑝 , where 1 < N < 10 and p is an integer.
Ex: Rewrite the number using scientific notation:
a)
Total spending in the federal budget is $3,900,000,000,000.
b) The diameter of a hydrogen nucleus is about 0.000 000 000 000 001 meter.
Computation:
To multiply and divide with scientific notation:
(𝑀 × 10𝑝 )(𝑁 × 10𝑞 ) = 𝑀𝑁 × 10𝑝+𝑞
𝑀 ×10𝑝
𝑁 ×10𝑞
=
𝑀
𝑁
× 10𝑝− 𝑞
Answers may need to be converted back to scientific notation.
Ex: Multiply (6 × 102 )(4 × 105 )
Ex: Divide
4.2 ×10−2
8.4 ×10−5
MAT 1043
3B Putting Numbers in Perspective
Page 2 of 2
PERSPECTIVE THROUGH ESITMATION:
An order of magnitude estimate specifies only a broad range of values, usually within one or two powers of ten.
Ex: Interpret the statement: “The number of stars in the galaxy is of the order 100 billion.”
Ex: Make an order of magnitude estimate of total annual spending on coffee in the US. (Reference: Consumerist.com report
that the average American worker spend $20 a week on coffee.)
PERSPECTIVE THROUGH COMPARISONS:
Comparing an unusually large or small number to a more understandable unit of measure.
Ex: Watch Video. How much is $100 billion?
a)
One semi-truck can hold 2 billion dollars (in $100 bills). How many trucks would we need?
b) Assume you spend $100 per second, how many years would it take?
DISCUSSION:
The current federal debt of the U.S.A. is approximately $18.3 trillion. The population of the U.S.A. is about 321 million. What is the
debt per person (do the calculations using scientific notation)? Compare this amount to something familiar to help put this value in
perspective. Reference: http://www.usdebtclock.org/.
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