Transcript Problem Solving Using Dimensional Analysis

Chapter 1
Measurements
1.6
Writing Conversion Factors
Copyright © 2009 by Pearson Education, Inc.
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Equalities
Equalities
• use two different units to describe the same measured
amount.
• are written for relationships between units of the metric
system, U.S. units, or between metric and U.S. units.
For example,
1m
=
1 lb
=
2.20 lb =
1000 mm
16 oz
1 kg
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Exact and Measured Numbers in
Equalities
Equalities between units in
• the same system of measurement are definitions
that use exact numbers.
• different systems of measurement (metric and U.S.)
use measured numbers that have significant figures.
Exception:
The equality 1 in. = 2.54 cm has been defined as an
exact relationship. Thus, 2.54 is an exact number.
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Some Common Equalities
39.4 in.
1.06 qt
946 mL = 1 qt
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Equalities on Food Labels
The contents of packaged foods
• in the U.S. are listed in both metric and U.S.
units.
• indicate the same amount of a substance in
two different units.
Copyright © 2009 by Pearson Education, Inc.
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Conversion Factors
A conversion factor is
• obtained from an equality.
Equality:
1 in. = 2.54 cm
• written as a fraction (ratio) with a numerator and
•
denominator.
inverted to give two conversion factors for every
equality.
1 in.
and 2.54 cm
2.54 cm
1 in.
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Learning Check
Write conversion factors from the equality for each
of the following.
A. liters and mL
B. hours and minutes
C. meters and kilometers
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Solution
Write conversion factors from the equality for each of the
following.
A. 1 L = 1000 mL
1L
and 1000 mL
1000 mL
1L
B. 1 h = 60 min
1h
and
60 min
60 min
1h
C. 1 km = 1000 m
1 km
1000 m
1000 m
1 km
and
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Conversion Factors in a Problem
A conversion factor
• may be obtained from information in a word problem.
• is written for that problem only.
Example 1:
The price of one pound (1 lb) of red peppers is $2.39.
1 lb red peppers and $2.39
$2.39
1 lb red peppers
Example 2:
The cost of one gallon (1 gal) of gas is $2.89.
1 gallon of gas and $2.89
$2.89
1 gallon of gas
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Percent as a Conversion Factor
A percent factor
• gives the ratio of the parts to the whole.
% =
parts x 100
whole
• uses the same unit in the numerator and denominator.
• uses the value 100.
• can be written as two factors.
Example: A food contains 30% (by mass) fat.
30 g fat
100 g food
and 100 g food
30 g fat
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Percent Factor in a Problem
The thickness of the skin fold at
the waist indicates 11% body
fat. What factors can be
written for percent body fat (in
kg)?
Percent factors using kg:
11 kg fat
and 100 kg mass
100 kg mass
11 kg fat
Copyright © 2009 by Pearson Education, Inc.
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Smaller Percents: ppm and ppb
Small percents are shown as ppm and ppb.
• Parts per million (ppm) = mg part/kg whole
Example: The EPA allows 15 ppm cadmium in food
colors
15 mg cadmium = 1 kg food color
=  g part/kg whole
Example: The EPA allows10 ppb arsenic in public
water
10  g arsenic = 1 kg water
• Parts per billion ppb
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Arsenic in Water
Write the conversion factors for 10 ppb arsenic
in public water from the equality
10  g arsenic = 1 kg water.
Conversion factors:
10  g arsenic
1 kg water
and
1 kg water
10  g arsenic
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Study Tip: Conversion Factors
An equality
• is written as a fraction (ratio).
• provides two conversion factors that are the
inverse of each other.
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Learning Check
Write the equality and conversion factors for each of the
following.
A. meters and centimeters
B. jewelry that contains 18% gold
C. One gallon of gas is $2.89
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Solution
A. 1 m = 100 cm
1m
and
100 cm
100 cm
1m
B. 100 g jewelry = 18 g gold
18 g gold and 100 g jewelry
100 g jewelry
18 g gold
C. 1 gal gas = $2.89
1 gal
and
$2.89
$2.89
1 gal
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Risk-Benefit Assessment
A measurement of toxicity is
• LD50 or “lethal dose.”
• the concentration of the substance that causes death
in 50% of the test animals.
• in milligrams per kilogram (mg/kg or ppm) of body mass.
• in micrograms per kilogram ( g/kg or ppb) of body
mass.
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Learning Check
The LD50 for aspirin is 1100 ppm. How many grams of
aspirin would be lethal in 50% of persons with a body
mass of 85 kg?
A. 9.4 g
B. 94 g
C. 94 000 g
Copyright © 2009 by Pearson Education, Inc.
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Solution
The LD50 for aspirin is 1100 ppm. How many grams of
aspirin would be lethal in 50% of persons with a body
mass of 85 kg?
B. 94 g
1100 ppm = 1100 mg/kg body mass
1100 mg
1g
85 kg 

= 94 g
kg
1000 mg
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