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A BIT DIFFERENT THAN USING PROPORTIONS!

Unit Analysis (or Dimensional Analysis) Problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. A BIT DIFFERENT THAN USING PROPORTIONS!. Doing Problems. Read problem completely

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A BIT DIFFERENT THAN USING PROPORTIONS!

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  1. Unit Analysis(or Dimensional Analysis)Problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value A BIT DIFFERENT THAN USING PROPORTIONS!

  2. Doing Problems • Read problem completely • Determine the measured quantities in the problem and the units • Determine units being requested • Determine conversion factor that will allow you to change to the new unit

  3. Rules • You must use Dimensional Analysis to solve conversion problems • Always show all your work • Include units • Make sure your units cancel out • Everything on the top is multiplied Everything on bottom is divided from the top

  4. Conversion Factors • A ratio (or fraction) derived from the equality between two different units that can be used to convert from one unit to the other. • Conversion factors always equal one because the two values are equal to each other.

  5. Conversion Factors 4 quarters 1 dollar = 1 = 1 1 dollar 4 quarters 60 minutes 1 hour = 1 = 1 1 hour 60 minutes 1 m 100 cm = 1 = 1 100 cm 1 m

  6. Converting from English to Metric Units and Vice versa Use conversion factors that are exact by definition 1 inch = 2.54 cm 1 ounce = 28.35 g 1 quart = 0.946L or 946 mL 1 meter = 39.37 inches 1 kilogram = 2.2 pounds Metric second = English second 1L = 1.0567 quarts

  7. Convert 62.0 inches to centimeters • First we need to map out what we are doing. 62.0 in  ___ cm

  8. Convert 62.0 inches to centimeters • Second we need to determine our conversion factor How many centimeters are in one inch? 2.54 cm = 1 in 1 in 2.54 cm Note: We could have also used that 1cm = .394 inch but as a general rule, the larger unit gets the 1! = 1 = 1 2.54 cm 1 in

  9. Convert 62.0 inches to centimeters • Third, we multiply our given by the conversion factor…making sure to arrange the conversion factor so that the units CANCEL! 62.0 in 2.54 cm X = 157.48 cm 1 in Note: Units that are both on the top and the bottom cancel

  10. Convert 62.0 inches to centimeters • Lastly, we make sure that we reached our “destination” and that we have the correct number of significant figures. 157.48 cm  157 cm Note: Conversions factors do not follow significant figure rules, they are not measured and do not show accuracy.

  11. Multiple Conversions • When conversions require several steps, Dimensional Analysis is extremely useful. It helps organize information so we can think through problems step-by-step.

  12. How many feet are in 965 cm? • 1. Map it out: 965 cm  ___ ft • 2. Find conversion factors:

  13. How many feet are in 965 cm? 965 cm 1 in 1 ft X X = 31.66  31.7 ft 2.54 cm 12 in

  14. Conversion w/only 2 Units

  15. Conversions with several units:

  16. You are cooking for a large group of people. You must change the recipe to accommodate all the guests. How many gallons will 384 teaspoons of vanilla extract occupy? • 1 Tablespoon (T) = 3 teaspoons (t) • 1 cup (c) = 16 Tablespoons • 1 pint (pt) = 2 cups • 1 quart (qt) = 2 pints • 1 gallon (gal) = 4 quarts

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