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.

Section 8.4

Dimensional Analysis

and Conversions to and from the Metric

System


What You Will Learn

Dimensional AnalysisUnit FractionsConversions to and from the Metric System

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Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement.

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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


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

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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


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)

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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)

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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

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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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Documents

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 8.4 Dimensional Analysis and Conversions to and from the Metric System