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 = 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 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 mg mg 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 mg mg 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 mg mg 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 mg mg 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 mg mg g
65.22 mg 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 mg mg g
65.22 mg g = g
1000 mg

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

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

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

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

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

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 eggs = 66 eggs
1 doz

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

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

52. Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet 2.01 miles 5280 feet 12 inches = inches 1 mile 1 feet Need correct # of sig figs!!!

53. Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet 2.01 miles 5280 feet 12 inches = inches 1 mile 1 feet Need correct # of sig figs!!! conversion factors do not affect the number of sig figs in answer *start with 3 sig figs = end with 3

54. Ex: Convert 2.01 miles to ___inches
1 mile = 5280 feet miles 5280 feet 12 inches = inches 1 mile 1 feet Need correct # of sig figs!!! conversion factors do not affect the number of sig figs in answer *start with 3 sig figs = end with 3

55. 834 hours to ___ months
834 hr

56. 834 hours to ___ months
834 hr hr Hours has to go on bottom to cancel, but I don’t know an hours to month conversion factor

57. 834 hours to ___ months
834 hr hr Hours has to go on bottom to cancel, but I don’t know an hours to month conversion factor But I do know hours to what?

58. 834 hours to ___ months
834 hr 1 day 24 hr

59. 834 hours to ___ months
834 hr 1 day 24 hr Now my unit is day, but I need month…so I need another step

60. 834 hours to ___ months
834 hr 1 day 24 hr What unit must go in the bottom of the next step?

61. 834 hours to ___ months
834 hr 1 day 24 hr day What is my day to month conversion factor?

62. 834 hours to ___ months
834 hr 1 day 1 month 24 hr 30 days

63. 834 hours to ___ months
834 hr 1 day 1 month = months 24 hr 30 days How many sig figs should there be in answer?

64. 834 hours to ___ months
834 hr 1 day 1 month = months 24 hr 30 days 1.16 months How many sig figs should there be in answer? 3

65. 0.143 hours to ____ seconds
0.143 hr

66. 0.143 hours to ____ seconds
0.143 hr 1 hr

67. 0.143 hours to ____ seconds
0.143 hr 60 min 1 hr

68. 0.143 hours to ____ seconds
0.143 hr 60 min 1 hr

69. 0.143 hours to ____ seconds
0.143 hr 60 min 1 hr

70. 0.143 hours to ____ seconds
0.143 hr 60 min 1 hr min

71. 0.143 hours to ____ seconds
0.143 hr 60 min sec 1 hr min

72. 0.143 hours to ____ seconds
0.143 hr 60 min 60 sec 1 hr 1 min

73. 0.143 hours to ____ seconds
0.143 hr 60 min 60 sec = seconds 1 hr 1 min

74. 0.143 hours to ____ seconds
0.143 hr 60 min 60 sec = seconds 1 hr 1 min 515 sec 3 sig figs!!