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Dimensional Analysis Two or More Conversion Factors

Dimensional Analysis Two or More Conversion Factors. If a problem requires two or more conversion factors, you must: Put all conversion factors into ONE equation. Show all conversion factors, even those that are 1:1. Do NOT combine two conversion factors into one!

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Dimensional Analysis Two or More Conversion Factors

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  1. Dimensional AnalysisTwo or More Conversion Factors • If a problem requires two or more conversion factors, you must: • Put all conversion factors into ONE equation. • Show all conversion factors, even those that are 1:1. • Do NOT combine two conversion factors into one! • Do the math at the very end, once the final desired units have been obtained.

  2. Dimensional AnalysisTwo or More Conversion Factors Example: A car traveled 200.0 ft in 5 s. What was its speed in mi/hr?

  3. Dimensional AnalysisTwo or More Conversion Factors Example: What is the height in inches of a person who is 2.0 m tall?

  4. Dimensional AnalysisTwo or More Conversion Factors Example: The density of pure aluminum is 2.70 g/cm3. Use dimensional analysis to calculate its density in lb/gal.

  5. Conversions Involving Volume • Common volume units include: • in3 • cm3 • m3 • liters • gallons • You must remember to cube both the number and the units in the conversion factor! 1 m3 = (100 cm)3 = 1003 cm3 1 in3 = (2.54 cm)3 = 2.543 cm3 Conversions involving squared or cubed units can be a little tricky!!!!

  6. Conversions With Volume Example: Convert 65.0 in3 to cm3.

  7. Conversions With Volume Example: The nominal density of wheat is 60. lb/bu. Calculate its density in g/cm3 if 1 bu = 1.244 ft3.

  8. Density/Mass/Volume Revisited • Calculations involving d, m, and V can be solved using dimensional analysis instead of remembering the formulas derived from d = m/V. • Think of density as a conversion factor relating mass and volume.

  9. Density/Mass/Volume Revisited Example: A 10-carat diamond has a mass of 2.0 g. If its density is 3.2 g/cm3, what is its volume?

  10. Conversion Factors From Problems Example: The recommended dose for a certain drug is 3.6 mg of drug per kg of body mass. Calculate the dose in milligrams for a 125-lb person.

  11. Conversion Factors From Problems Example: Car batteries contain sulfuric acid, which is commonly referred to as “battery acid.” Calculate the number of grams of sulfuric acid in 0.225 L of battery acid if the solution has a density of 1.272 g/mL and is 35.9% sulfuric acid by mass.

  12. Problem Solving Steps • Make a list of the information given (including units). • Decide what unknown you’re solving for and the appropriate units. • How do you convert from what you know to what you’re trying to find? • Definition? • Equation? • Conversion Factor? • Use dimensional analysis to solve the problem. • Write the answer with the correct number of significant figures and units. • Does the answer make sense?

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