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Metric System Conversions: Dimensional Analysis Basics

Learn how to convert units of measurement using Dimensional Analysis and Unit Fractions. Master length, area, volume, weight conversions, and dosage calculations in this comprehensive guide.

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Metric System Conversions: Dimensional Analysis Basics

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  1. Section 8.4Dimensional Analysis and Conversions to and from the Metric System

  2. What You Will Learn • Dimensional Analysis • Unit Fractions • Conversions to and from the Metric System

  3. Dimensional Analysis • Dimensional analysisis a procedure used to convert from one unit of measurement to a different unit of measurement.

  4. Dimensional Analysis A unit fractionis any fraction in which the numerator and denominator contain different units and the value of the fraction is 1. Examples of unit fractions:

  5. 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 U.S. Customary Units

  6. Example 1: Using Dimensional Analysis A container contains 26 ounces of salt. Convert 26 ounces to pounds. Solution Thus, 26 oz equals 1.625 lb.

  7. Example 3: Using Several Unit Fractions Convert 60 miles per hour to feet per second. Solution

  8. Conversion to and from the Metric System - Length

  9. Conversion to and from the Metric System - Area

  10. Conversion to and from the Metric System - Area

  11. Conversion to and from the Metric System - Volume

  12. Conversion to and from the Metric System – Weight (Mass)

  13. Example 4: Volume and Length Conversions a) A recipe requires 3½ cups of chicken broth. How many liters does this amount equal? Solution

  14. Example 4: Volume and Length Conversions b) A man measures 1.86 m. What is his height in feet? Solution

  15. Example 5: Area Conversion An area of 54.62 hectares is for sale. Find the area in acres. Solution

  16. 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.

  17. Example 7: Administering a Medicine b) How many ounces is this dosage equivalent to? Solution

  18. 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?

  19. Example 10: Determining Dosage by Weight Solution 30 mg, 136 lb Amount of drug

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