Section 8.4
Dimensional
Analysis and
Conversions
to and from
the Metric
System
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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
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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
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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.
8.4-6
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Example 3: Using Several Unit
Fractions
Convert 60 miles per hour to feet per
second.
8.4-8
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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)
8.4-10
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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)
8.4-11
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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)
8.4-12
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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)
8.4-13
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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)
8.4-14
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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?
8.4-15
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Example 4: Volume and Length
Conversions
b) A man measures 1.86 m. What is
his height in feet?
8.4-17
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Example 5: Area Conversion
An area of 54.62 hectares is for sale.
Find the area in acres.
8.4-19
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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?
8.4-21
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Example 7: Administering a
Medicine
b) How many ounces is this dosage
equivalent to?
8.4-23
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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?
8.4-25
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