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Dimensional Analysis

Dimensional Analysis. Factor Labeling. Dimensional Analysis . This is a method of problem-solving which ___ focuses ______ on the units . Dimensional Analysis . This is a method of problem-solving which ___ focuses ______ on the units .

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Dimensional Analysis

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  1. Dimensional Analysis Factor Labeling

  2. Dimensional Analysis • This is a method of problem-solving which ___focuses______ on the units.

  3. Dimensional Analysis • This is a method of problem-solving which ___focuses______ on the units. • Helps you set up equations correctly → Solve for units as wells as numbers

  4. Dimensional Analysis • ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units.

  5. Dimensional Analysis • ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units. • Always equal to __1____.

  6. Dimensional Analysis • ____A conversion factor___________ is a ratio of equivalent values used to express the same quantity in different units. • Always equal to __1____. • Used to convert from one unit to the other.

  7. Dimensional Analysis Set up the problem so the units will cancel as you solve it.

  8. Dimensional Analysis Example: 1 Liter = 1000 milliliters

  9. Dimensional Analysis Example: 1 Liter = 1000 milliliters This equality can be converted into __2__ conversion factors

  10. Dimensional Analysis Example: 1 Liter = 1000 milliliters This equality can be converted into __2__ conversion factors. 1 L or 1000 mL

  11. Dimensional Analysis Example: 1 Liter = 1000 milliliters This equality can be converted into __2__ conversion factors. 1 L or 1000 mL 1000 mL 1 L

  12. To solve problems with dimensional analysis: • Put given value on __top__ of fraction bar

  13. To solve problems with dimensional analysis: • Put given value on __top__ of fraction bar • Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit.

  14. To solve problems with dimensional analysis: • Put given value on __top__ of fraction bar • Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit. • Set up conversion factor with __desired unit_ on top and ___given__ unit on __bottom__ so given units cancel.

  15. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __

  16. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__

  17. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg

  18. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g

  19. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g • 65.22 mg

  20. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g • 65.22 mg {pick a conversion factor so that the given units (mg) cancel}

  21. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g • 65.22 mg

  22. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g • 65.22 mg 1 g 1000 mg

  23. Example: Convert 65.22 mg to ___g • Given: __65.22 mg __ • Equality: __1 g = 1000 mg__ so…. 2 conversion factors: 1 g or 1000 mg 1000 mg 1 g • 65.22 mg 1 g = 0.06522 g 1000 mg

  24. Practice: 0.84 m to _____ cm Given: __0.84 m__

  25. Practice: 0.84 m to _____ cm Given: __0.84 m__ Equality: 1 m = 100 cm which unit should go on the bottom?

  26. Practice: 0.84 m to _____ cm Given: __0.84 m__ Equality: 1 m = 100 cm which unit should go on the bottom? Answer: the unit you want to cancel: m

  27. Practice: 0.84 m to _____ cm Given: __0.84 m__ Equality: 1 m = 100 cm which unit should go on the bottom? Answer: the unit you want to cancel: m so use: 100 cm 1 m

  28. Practice: 0.84 m to _____ cm Given: __0.84 m__ so use: 100 cm 1 m 0.84 m

  29. Practice: 0.84 m to _____ cm Given: __0.84 m__ so use: 100 cm 1 m 0.84 m 100 cm 1 m

  30. Practice: 0.84 m to _____ cm Given: __0.84 m__ so use: 100 cm 1 m 0.84 m 100 cm = 84 cm 1 m

  31. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz

  32. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz Equality: 1 doz = 12 eggs

  33. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz Equality: 1 doz = 12 eggs We want doz to cancel:

  34. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz Equality: 1 doz = 12 eggs We want doz to cancel: so put doz on bottom

  35. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz Equality: 1 doz = 12 eggs We want doz to cancel: so use: 12 eggs 1 doz

  36. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz 5.5 doz

  37. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz 5.5 doz 12 eggs 1 doz

  38. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz 5.5 doz 12 eggs = 66 eggs 1 doz

  39. Practice: 5.5 dozen eggs to single eggs Given: 5.5 doz 5.5 doz 12 eggs = 66 eggs 1 doz conversion factors do not affect the number of sig figs in answer *start with 2 sig figs = end with 2

  40. Sometimes you may need more than __1___conversion factor

  41. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles

  42. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles

  43. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 1 mile

  44. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 1mile

  45. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 1mile

  46. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 1mile Now our answer is in feet…but we want inches So…we need another step!!

  47. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 1mile

  48. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 1mile feet

  49. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 12 inches 1mile 1 feet

  50. Ex: Convert 2.01 miles to ___inches 1 mile = 5280 feet 2.01 miles 5280 feet 12 inches 1mile 1 feet

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