2. Conversion Factors and Unit Cancellation

3. A physical quantity must include: Number + Unit + Unit

4. Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot = 12 inches

5. Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1

6. Calculation Corner: Unit Conversion 1 foot = 12 inches 1 foot 12 inches = 1 12 inches 1 foot = 1

7. Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors”

8. Calculation Corner: Unit Conversion 1 foot 12 inches 1 foot “Conversion factors” 3 feet 3 feet 12 inches 12 inches 1 foot 1 foot = 36 inches ( ( ) ) ( ( ) )

9. Dimensional Analysis A mathematical way to convert one unit to another. This works for metric units and non-metric (English) units. This works by taking the unit you are given and multiplying it by a conversion factor. CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

10. Example 1: Convert 3m to cm Given Conversion Factor For meters to cancel out, meters in the conversion factor must be on the opposite side of the fraction (fence). CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 3m 100 cm 1m Multiply every number on top of the fence and divide by the bottom.

11. Example 2: Convert 1516 g to kg conversion factor CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 1516 g 1 kg 1000 g

12. Whiteboard Problem 1 Convert 1200 cm to m. CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

13. Example 4: Convert 7200mm to km 7200 mm =.0072 km CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 10 mm 1 cm 1 km 100,000 cm

14. Non-Metric (English) Unit Conversions Common Conversion Factors –5280 ft = 1 mile –12 in = 1 ft –1 mile = 1600 m –1 in = 2.54 cm –3 ft = 1 yard CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. English to Metric conversion factors

15. Example 4: Convert 2 miles to ft CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 2 mi 5280 ft 1 mi

16. Whiteboard Problem 4 Convert 5 ft to cm CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula.

17. Example 5: Convert 5 ft to cm CLE.3231.Math.1 Graph relationships and functions between manipulated (independent) variables and responding (dependent) variables.CLE.3231.Math.2 Solve for variables in an algebraic formula. 5 ft 12 in 1 ft 2.54 cm 1 in

18. How many cm are in 1.32 meters? applicable conversion factors: equality: or X cm = 1.32 m= 1 m = 100 cm ______1 m 100 cm We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. ______ 1 m 100 cm () ______ 1 m 100 cm 132 cm (or 0.01 m = 1 cm)

19. How many meters is 8.72 cm? applicable conversion factors: equality: or X m = 8.72 cm= 1 m = 100 cm ______1 m 100 cm Again, the units must cancel. ______ 1 m 100 cm () ______ 0.0872 m 1 m 100 cm

20. How many feet is 39.37 inches? applicable conversion factors: equality: or X ft = 39.37 in= 1 ft = 12 in ______1 ft 12 in Again, the units must cancel. () ____ 3.28 ft 1 ft 12 in ______ 1 ft 12 in

21. How many kilometers is 15,000 decimeters? X km = 15,000 dm= 1.5 km () ____ 1,000 m 1 km 10 dm 1 m () ______

22. How many seconds is 4.38 days? = 1 h 60 min24 h 1 d1 min 60 s ____ ()() () _____ X s = 4.38 d 378,432 s3.78 x 10 5 s If we are accounting for significant figures, we would change this to…

23. The steps to follow Now we are ready to solve problems using the factor label method. The steps involved are: 1.Write down the desired quantity/units 2.Equate the desired quantity to given quantity 3.Determine what conversion factors you can use (both universal and question specific) 4.Multiply given quantity by the appropriate conversion factors to eliminate units you don’t want and leave units you do want 5.Complete the math

24. Factor label example Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) First write down the desired quantity # km

25. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Next, equate desired quantity to the given quantity # km= 47 mi Factor label example

26. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Now we have to choose a conversion factor # km= 47 mi Factor label example

27. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) What conversion factors are possible? # km= 47 mi 1 km 0.621 mi 1 km Factor label example

28. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Pick the one that will allow you to cancel out miles # km= 47 mi 1 km 0.621 mi 1 km Factor label example

29. Pick the one that will allow you to cancel out miles Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) # km= 47 mi 1 km 0.621 mi 1 km Factor label example

30. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Multiply given quantity by chosen conversion factor # km= 47 mi 1 km 0.621 mi 1 km Factor label example

31. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Multiply given quantity by chosen conversion factor # km= 47 mi x 1 km 0.621 mi Factor label example

32. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Cross out common factors # km= 47 mi x 1 km 0.621 mi Factor label example

33. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Cross out common factors # km= 47 x 1 km 0.621 Factor label example

34. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Are the units now correct? # km= 47 x 1 km 0.621 Factor label example

35. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Yes. Both sides have km as units. # km= 47 x 1 km 0.621 Factor label example

36. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Yes. Both sides have km as units. # km# km = 47 x 1 km 0.621 # km Factor label example

37. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) Now finish the math. # km= 47 x 1 km 0.621 = 75.7 km Factor label example

38. Q - How many kilometers are in 47 miles? (note: 1 km = 0.621 miles) The final answer is 75.7 km # km= 47 x 1 km 0.621 = 75.7 km Factor label example

39. Summary The previous problem was not that hard In other words, you probably could have done it faster using a different method However, for harder problems the factor label method is easiest

40. Real Life Chemistry Keys Real Life Chemistry http://www.unit5.org/chemistry/intro.html

41. Simple Math with Conversion Factors

42. Measured dimensions of a rectangle: Find area of rectangle. A = L. W = (9.70 cm)(4.25 cm) length (L) = 9.70 cm width (W) = 4.25 cm L W = Example Problem 41.2cm 2. cm

43. Convert 41.2 cm 2 to m 2. 100 cm 1 m () ______ X m 2 = 41.2 cm 2 X m 2 = 41.2 cm. cm Recall that…41.2 cm 2 = 41.2 cm. cm 100 cm 1 m () ______ X m 2 = 41.2 cm 2 =0.412 m 2 =0.412 cm. m WRONG! () ______ 100 cm 1 m =0.00412 m 2 () ______ 100 cm 1 m 2 =0.00412 m 2

44. Convert 41.2 cm 2 to mm 2. X mm 2 = 41.2 cm 2 X mm 2 = 41.2 cm. cm Recall that…41.2 cm 2 = 41.2 cm. cm 1 cm 10 mm () _____ =4,120 mm 2 = 1 cm 10 mm () _____ 4,120 mm 2 1 cm 10 mm 2 () _____

45. Measured dimensions of a rectangular solid: Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L. W. H = (15.2 cm)(3.7 cm)(8.6 cm) =480cm 3

46. Convert to m 3. X m 3 = 480 cm 3 =0.000480 m 3 100 cm 1 m 3 () _____ X m 3 = 480 cm 3 = X m 3 = 480 100 cm 1 m () _____ 100 cm 1 m () _____ 100 cm 1 m () _____ = or cm. cm. cm 1 m 1000000 cm ( ) _________ 3 3 4.80 x 10 -4 m 3 or 3 2 cm

47. Measured dimensions of a rectangular solid: Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L. W. H = (0.152 m)(0.037 m)(0.086 m) =0.000480 m 3 0.152 m 0.037 m 0.086 m Convert to m 3...

48. Convert to mm 3.

49. By what factor do mm and cm differ? 10 By what factor do mm 2 and cm 2 differ? 100 By what factor do mm 3 and cm 3 differ? 1,000 1 cm = 10 mm (1 cm) 2 = (10 mm) 2 1 cm 2 = 100 mm 2 (1 cm) 3 = (10 mm) 3 1 cm 3 = 1000 mm 3

50. Conversion Factors Keys Conversion Factors http://www.unit5.org/chemistry/intro.html