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Mastering Unit Analysis: Conversions & Factor Label Method

Understand unit analysis (or dimensional analysis) through conversion examples. Learn how to convert units for different measurements with practical scenarios. Enhance your math skills with this detailed guide.

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Mastering Unit Analysis: Conversions & Factor Label Method

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  1. UnitAnalysisSupplementto Math 60Chapter 3 Cathy Mulleary Summer 2013

  2. Unit Analysis Alternate names for the same process are: • Unit Conversions • Factor Label Method • Unit Factor Method • Dimensional Analysis

  3. Unit analysis uses the same concept as “equivalent fractions.” Multiplying a quantity by a ratio equal to one changes the looks of the quantity without changing its value.

  4. The process of unit analysis focuses on converting to the units necessary to answer a question. Example: How many feet are there in 360 inches? In order to answer the question, I need to know a “conversion fact.” In this case, the fact is: 1 foot = 12 inches. Start with the value we are “converting” (writing it as a fraction is VERY helpful). Always include the units. This is required. Next, multiply the starting value by the conversion fact written as a fraction. Now, it’s just arithmetic.

  5. The question is: How do I know how to write the conversion fact? What goes on top? What goes on the bottom? • You must arrange the conversion fact so the units “drop out.” • In the previous example, reversing the top and bottom wouldn’t work because the units don’t get eliminated.

  6. Example: How many centimeters are there in 23 feet? The conversion facts needed are: 1 in = 2.54 cm 1 ft = 12 in Choosing the right conversion facts requires you to “figure out” how am I going to get from cm to ft with the conversions facts I know or have available. Note: It is NOT acceptable for you to look up a conversion; although they are readily available on the internet. You to be able to figure it out knowing just a few facts.

  7. Example: Rewrite 3521 mL as quarts. The conversion facts needed are: 1tsp = 5mL 1c = 48tsp 4c = 1qt Rounded to the hundredths place this is 3.67 qt.

  8. Last example: Convert 60 mph to kilometers per hour; round to the nearest hundredth. Conversion facts needed 1mi=1760yd Kmph is a common abbreviation for

  9. Now you try: Katelyn can bicycle at a rate of 100 yards in 15 seconds, what is her rate in miles per hour? (round to the nearest tenth) Necessary conversions: 1mi = 1760yd 1min = 60sec 1hr = 60min = 13.6 mph

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