5 5 Customary Units Dimensional Analysis

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Chapter 5, Section 5: Customary Units and Dimensional Analysis. Short.

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5 5 Customary Units Dimensional Analysis

  1. 1. Review of Customary Units, Fractions, and Dimensional Analysis. By Ms. Dewey-Hoffman February 23, 2020 Chapter 5, Section 5 (if you must know)
  2. 2. Example of Conversion Factors <ul><li>To find a COMMON DENOMINATOR </li></ul><ul><li>between Two Fractions , </li></ul><ul><li>you MULTIPLY one or both </li></ul><ul><li>fractions by a Conversion Factor . </li></ul>A Conversion Factor is always equal to 1 .
  3. 3. This is the Same with Conversion Factors in Converting Units! <ul><li>Use Equivalent Units To Write A Conversion Factor. </li></ul>Like: 12 inches = 1 foot. They Are Equivalent! Also: 4 quarts = 1 gallon. They Are Equivalent! Also: 24 hours = 1 day. They Are Equivalent!
  4. 4. Turn The Conversions Into Fractions…They’re Equivalent <ul><li>Just Write These Equivalents to Make a Fraction that is Equal to 1. </li></ul>12 inches = 1 1 foot 2 cups = 1 8 Fluid Ounces
  5. 5. Dimensional Analysis <ul><li>The process of analyzing units to decide which conversion factors to use. </li></ul>When you are looking at the Legend on your handout, that’s Dimensional Analysis!
  6. 6. This is a Fraction Bar These Bars mean Multipl-ication and separate fractions or Conversion Factors. 10 quarts = ? gallons 10 Quarts ? Gallons Conversion Factor Goes Here 4 Quarts 1 Gallon Now turn it into a Fraction/Multiplication Problem 10  ¼ = 2 ½ gallons 10 quarts = 2 ½ gallons
  7. 7. This is a Fraction Bar These Bars mean Multipl-ication and separate fractions or Conversion Factors. Dealing with Mixed Numbers and Conversions? 3 3/16 yards = ? inches 1) Change Mixed Number to an Improper Fraction, then Convert. 51 Yards 1 Yard 3 Feet 1 Foot 12 Inches 16 2) Take the answer and Change to a Mixed Number. Notice how the IMPROPER Fraction looks like a Fraction on the T graph. (51  3  12)  (16  1  1) = 114.75 or 114 ¾
  8. 8. To Compare Different Units… <ul><li>Change ONE Unit into the other and see which is bigger, less, or equal. </li></ul><ul><li>Inequalities Anyone? </li></ul>10 Gallons ____ 42 Quarts <ul><li>42 Quarts is how many gallons? </li></ul><ul><li>4 Quarts for every 1 Gallon. (42/4 = 10 ½ Gallons) </li></ul><ul><li>Which is bigger? 42 Quarts or 10 Gallons? </li></ul><

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