Section 8.4
Dimensional
Analysis and
Conversions
to and from
the Metric
System
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
What You Will Learn
Dimensional Analysis
Unit Fractions
Conversions to and from the Metric
System
8.4-2
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Dimensional Analysis
Dimensional analysis is a procedure
used to convert from one unit of
measurement to a different unit of
measurement.
8.4-3
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Dimensional Analysis
A unit fraction is any fraction in which
the numerator and denominator
contain different units and the value of
the fraction is 1.
Examples of unit fractions:
16 oz
1 lb
8.4-4
1 hr
60 min
12 in.
1 ft
Copyright 2013, 2010, 2007, Pearson, Education, Inc.
U.S. Customary Units
U.S. Customary Units
1 foot = 12 inches
1 quart = 2 pints
1 yard = 3 feet
1 gallon = 4 quarts
1 mile = 5280 feet
1 minute = 60 seconds
1 pound = 16 ounces
1 hour = 60 minutes
1 ton = 2000 pounds
1 day = 24 hours
1 cup (liquid) = 8 fluid ounces
1 year = 365 days
1 pint = 2 cups
8.4-5
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Example 1: Using Dimensional
Analysis
A container contains 26 ounces of salt.
Convert 26 ounces to pounds.
Solution
 1 lb  26
26 oz = 26 oz 
=
lb

 16 oz  16
= 1.625 lb
(
)
Thus, 26 oz equals 1.625 lb.
8.4-6
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Example 3: Using Several Unit
Fractions
Convert 60 miles per hour to feet per
second.
Solution

mi   5280 ft   1 hr
mi 
=  60
60





hr   1 mi   3600 sec 
hr 
(60)(5280) ft
ft
=
= 88
(1)(3600) sec
sec
8.4-7
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Conversion to and from the
Metric System - Length
LENGTH
U.S. to Metric
1 inch (in.) ≈ 2.54 centimeters (cm)
1 foot (ft) ≈ 30 centimeters (cm)
1 yard (yd) ≈ 0.9 meter (m)
1 mile (mi) ≈ 1.6 kilometers (km)
8.4-8
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Conversion to and from the
Metric System - Area
AREA
U.S. to Metric
1 square inch (in.2) ≈ 6.5 square centimeters (cm2)
1 square foot (ft2) ≈ 0.09 square meter (m2)
1 square yard (yd2) ≈ 0.8 square meter (m2)
1 square mile (mi2) ≈ 2.6 square kilometers (km2)
1 acre ≈ 0.4 hectare (ha)
8.4-9
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Conversion to and from the
Metric System - Area
VOLUME
U.S. to Metric
1 teaspoon (tsp) ≈ 5 milliliters (ml)
1 tablespoon (tbsp) ≈ 15 milliliters (ml)
1 fluid ounce (fl oz) ≈ 30 milliliters (ml)
1 cup (c) ≈ 0.24 liter (l)
1 pint (pt) ≈ 0.47 liter (l)
8.4-10
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Conversion to and from the
Metric System - Volume
VOLUME
U.S. to Metric
1 quart (qt) ≈ 0.95 liter (l)
1 gallon (gal) ≈ 3.8 liters (l)
1 cubic foot (ft3) ≈ 0.03 cubic meter (m3)
1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)
8.4-11
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Conversion to and from the
Metric System – Weight (Mass)
WEIGHT OR MASS
U.S. to Metric
1 ounce (oz) ≈ 28 grams (g)
1 pound (lb) ≈ 0.45 kilogram (kg)
1 ton (T) ≈ 0.9 tonne (t)
8.4-12
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Example 4: Volume and Length
Conversions
a) A recipe requires 3½ cups of
chicken broth. How many liters does
this amount equal?
Solution
 0.24 l 
3.5 cups = 3.5 cups 

 1 cup 

= (3.5)(0.24)l 
= 0.84l

8.4-13
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Example 4: Volume and Length
Conversions
b) A man measures 1.86 m. What is
his height in feet?
Solution
 1 yd   3 ft 
1.86 m = 1.86 m 



 0.9 m   1 yd 
(1.86)(3)
=
ft = 6.2 ft
0.9
8.4-14
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Example 5: Area Conversion
An area of 54.62 hectares is for sale.
Find the area in acres.
Solution
 1 acre 
54.62 ha = 54.62 ha 

 0.4 ha 
54.62
=
acres = 136.55 acres
0.4
8.4-15
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Example 7: Administering a
Medicine
A nurse must administer 4 cc of
codeine elixir to a patient.
a) How many milliliters of the drug will
be administered?
Solution
Since 1 cc = 1 ml, the nurse will
administer 4 ml of the drug.
8.4-16
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Example 7: Administering a
Medicine
b) How many ounces is this dosage
equivalent to?
Solution
 1 fl oz 
4 ml = 4 ml 

30
ml



4
=
fl oz ≈ 0.13 fl oz
30
8.4-17
(
)
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Example 10: Determining Dosage
by Weight
Drug dosage is often administered
according to a patient’s weight. For
example, 30 mg of the drug
vancomycin is to be given for each
kilogram of a person’s weight. If
Martha Greene, who weighs 136 lb, is
to be given the drug, what dosage
should she be given?
8.4-18
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Example 10: Determining Dosage
by Weight
Solution
30 mg, 136 lb
 0.45 kg 
= 61.2 kg
136 lb = 136 lb 

 1 lb 
 30 mg 
Amount
=
1836
mg
= 61.2 kg 

of drug
 1 kg 
8.4-19
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