Transcript Section 3B Putting Numbers in Perspective

Section 3B Part II
Putting Numbers in
Perspective
Pages 152-171
3-B
To appreciate really, really large numbers
and really, really small numbers, we must
“put them in perspective.”
Three Techniques
• Perspective through Estimation
• Perspective through Comparisons
• Perspective through Scaling
3-B
1. Perspective Through Estimation
pg157 How high is 1000 feet?
Each story ≈ 10 feet (floor to ceiling)
So 100-story building ≈ 1000 feet
(Empire State Building is 102 stories and 1250
feet so…. one story = 10-12 feet)
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Example Which is larger – the height of a 10-story apartment
building, or the length of a football field? By how much?
Each story ≈ 10-12 feet high
10 story building ≈ 10 stories  10-12 ft/story = 100 - 120 ft
Football field = 100 yards = 100 yd × 3ft/yd
= 300 ft
The football field is almost 3 times as long as the 10-story
building is high.
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Definition: An order of magnitude estimate
specifies only a broad range of values, such as
“in the tens of thousands” or “in the millions.”
The population of the U.S. is “on the order of
300 million”.
(2000 census says 281 million)
Ex3/158 Make an order of magnitude estimate of
the total amount of money spent each year on
ice cream in the US.
Assumptions:
≈ $1 per serving
≈ 1 serving of ice cream per week.
52 weeks per year
≈ $52 per person per year
≈ 300 million Americans
So, 300 million  52 = 300 x 106 x 5.2 x 10
= 3 x 108 x 5.2 x 10
= 15.6 x 109
≈ $15.6 billion spent by Americans for ice cream each
year.
3-B
2. Perspective Through Comparison
(compare to something easily understandable)
pg 159 How much is $100 billion?
$100 billion (= $100  109 )
= $1.0×1011
How long would it take to count this many $1 bills –
at a rate of 1 bill per second?
 1 min   1 hr   1 day   1 yr 
1.0  10 sec  




60
sec
60min
24hr
365
days

 
 
 

11
 3,171 years
3-B
Comparison for Unfamiliar Units
3-B
Ex4/160 Compare the U.S. population to
world population and the U.S. energy
consumption to world energy
consumption.
Population
U.S.
300 million
Energy
Consumption
1×1020 joules
World
6 billion
5×1020 joules
(300 million)/(6 billion) = (3x108)/(6x109) = .5x10(-1) = .05 = 5%
The US population is approximately 5% of the 20
world population.
U.S.energy 110
1


10
World
energy 5 10
5
(1x1020)/(5x1020) = 0.20
= 20%
The US population consumes 20% of the world’s energy.
3. Perspective Through
Scaling
3 common ways of expressing scales
• Verbally (1 in = 1 mi)
• Graphically (marked mini-ruler)
• Scale ratio (1 to 92,160)
3-B
3-B
Graphically (marked mini-ruler)
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Finding the scale ratio:
EX6/161 A city map states 1 in = 1 mi.
What is the scale ratio for the map?
1 mile x 5280 ft/mile x 12 in/ft = 63,360 inches
One map inch represents 63360 ground inches.
The scale ratio for this map is 1 to 63360.
Actual distances are 63360 times map distances.
Timelines
EX9/163 Human civilization, at least since the time of ancient
Egypt is on the order of 5000 years old. The age of the
Earth is on the order of 5 billion years. Suppose we use the
length of a football field or about 100 meters as a timeline
to represent the age of the Earth. How far from the line’s
end would human civilization begin.
100 meters = 5 x 109 years
5000 years = 5 x 103 years x 100 meters
5x109 years
= 1 x 10(-4) meters
= .0001 meters = 0.1 mm
WOW! On a timeline where the Earth’s history stretches
the length of a football field, human civilization appears
only in the final tenth of a millimeter
3-B
More Practice
pg 164 How large is a University
with 25,000 students?
IDEA: Suppose the President plans to meet with 5
students for lunch, 5 times per week. How long will it
take her to meet with the entire student body?
She meets with 5x5 = 25 students/week
25,000/25 = 1000 weeks to meet entire student body
1000 weeks/(50 weeks per year)
= 20 years of lunches !!
More Practice
49/165 Make an order of magnitude
estimate for the amount of gas an
average adult driver uses per year.
71/170 Approximately 1.4 million violent crimes are
reported to police every year. How many violent
crimes are reported every hour?
75/166 The national debt was $8.5 trillion at the end
of 2006. Express this quantity as the height of a stack
of one-dollar bills. (10 dollar bills = 1 mm).
3-B
Homework
Pages 169-171
# 42,46,50,65,69,72,74,77
Important Numbers
• Current US Population ≈ 281 million (300 million)
• Approximate distance across U.S = 4000 km
• The average person can walk 10-15 miles per day.
Pankratova Legs
52 inches
He Pingping Height
29.37 inches
Percent Of
29.37/52 = .565
He Pingping’s Height is 56.5% of Pnakratova’s Leg Length