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

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Presentation on theme: "Dimensional Analysis Factor Labeling. Dimensional Analysis This is a method of problem-solving which ___focuses______ on the units."— Presentation transcript:

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 Lor 1000 mL

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

12 To solve problems with dimensional analysis: 1.Put given value on __top__ of fraction bar

13 To solve problems with dimensional analysis: 1.Put given value on __top__ of fraction bar 2.Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit.

14 To solve problems with dimensional analysis: 1.Put given value on __top__ of fraction bar 2.Determine what __conversion factor__ you can use that has both the given unit & ______desired__ unit. 3.Set up conversion factor with __desired unit_ on top and ___given__ unit on __bottom__ so given units cancel.

15 Example: Convert mg to ___g 1.Given: __65.22 mg __

16 Example: Convert mg to ___g 1.Given: __65.22 mg __ 2.Equality: __1 g = 1000 mg__

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

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

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

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

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

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

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

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 dont 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 dont 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 hr

66 0.143 hours to ____ seconds hr 1 hr

67 0.143 hours to ____ seconds hr 60 min 1 hr

68 0.143 hours to ____ seconds hr 60 min 1 hr

69 0.143 hours to ____ seconds hr 60 min 1 hr

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

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

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

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

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


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