copyright 2013, 2010, 2007, pearson, education, inc. section 8.4 dimensional analysis and...
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
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 AnalysisUnit FractionsConversions to and from the Metric System
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Copyright 2013, 2010, 2007, Pearson, Education, Inc.
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
12 in.
1 ft
1 hr
60 min8.4-4
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U.S. Customary Units
1 pint = 2 cups 1 year = 365 days1 cup (liquid) = 8 fluid ounces
1 day = 24 hours1 ton = 2000 pounds
1 hour = 60 minutes
1 pound = 16 ounces
1 minute = 60 seconds
1 mile = 5280 feet
1 gallon = 4 quarts
1 yard = 3 feet
1 quart = 2 pints1 foot = 12 inches
U.S. Customary Units
8.4-5
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Example 1: Using Dimensional AnalysisA container contains 26 ounces of salt. Convert 26 ounces to pounds.
Solution
26 oz 26 oz 1 lb
16 oz
26
16 lb
Thus, 26 oz equals 1.625 lb.
1.625 lb
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Example 3: Using Several Unit FractionsConvert 60 miles per hour to feet per second.
Solution
60
mi
hr 60
mi
hr
5280 ft
1 mi
1 hr
3600 sec
(60)(5280)
(1)(3600)
ft
sec 88
ft
sec8.4-7
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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)
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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)
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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)
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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 Conversionsa) A recipe requires 3½ cups of chicken broth. How many liters does this amount equal?
Solution
3.5 cups 3.5 cups
0.24 l
1 cup
(3.5)(0.24)l 0.84l
8.4-13
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Example 4: Volume and Length Conversionsb) A man measures 1.86 m. What is his height in feet?
Solution
1.86 m 1.86 m
1 yd
0.9 m
3 ft
1 yd
(1.86)(3)
0.9 ft 6.2 ft
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Example 5: Area Conversion
An area of 54.62 hectares is for sale. Find the area in acres.
Solution
54.62 ha 54.62 ha
1 acre
0.4 ha
54.62
0.4 acres 136.55 acres
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Example 7: Administering a MedicineA 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.
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Example 7: Administering a Medicineb)How many ounces is this dosage
equivalent to?
Solution
4 ml 4 ml 1 fl oz
30 ml
4
30 fl oz 0.13 fl oz
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Example 10: Determining Dosage by WeightDrug 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?
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Example 10: Determining Dosage by WeightSolution30 mg, 136 lb
136 lb 136 lb
0.45 kg
1 lb
61.2 kg
61.2 kg
30 mg
1 kg
1836 mg
Amountof drug
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