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**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

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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.

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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:

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**U.S. Customary Units 1 pint = 2 cups 1 year = 365 days**

1 cup (liquid) = 8 fluid ounces 1 day = 24 hours 1 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 pints 1 foot = 12 inches U.S. Customary Units

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**Example 1: Using Dimensional Analysis**

A container contains 26 ounces of salt. Convert 26 ounces to pounds. Solution Thus, 26 oz equals lb.

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**Example 3: Using Several Unit Fractions**

Convert 60 miles per hour to feet per second. Solution

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**Conversion to and from the Metric System - 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**

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**

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 Conversions**

a) A recipe requires 3½ cups of chicken broth. How many liters does this amount equal? Solution

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**Example 4: Volume and Length Conversions**

b) A man measures 1.86 m. What is his height in feet? Solution

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**Example 5: Area Conversion**

An area of hectares is for sale. Find the area in acres. Solution

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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.

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**Example 7: Administering a Medicine**

b) How many ounces is this dosage equivalent to? Solution

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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?

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**Example 10: Determining Dosage by Weight**

Solution 30 mg, 136 lb Amount of drug

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