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Conversion Factors and Unit Cancellation

Conversion Factors and Unit Cancellation. A physical quantity must include:. Number. + Unit. Calculation Corner: Unit Conversion. 1 foot = 12 inches. Calculation Corner: Unit Conversion. 1 foot = 12 inches. 1 foot. = 1. 12 inches. Calculation Corner: Unit Conversion.

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Conversion Factors and Unit Cancellation

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  1. Conversion FactorsandUnit Cancellation

  2. A physical quantity must include: Number + Unit

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

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

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

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

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

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

  9. 0.0872 m 100 cm ______ 1 m ______ 1 m 100 cm ______ ( ) 1 m 100 cm equality: 1 m = 100 cm How many meters is 8.72 cm? applicable conversion factors: or X m = 8.72 cm = Again, the units must cancel.

  10. 1 ft ______ 1 ft 12 in 12 in ( ) ______ 12 in ____ 1 ft 3.28 ft equality: 1 ft = 12 in How many feet is 39.37 inches? applicable conversion factors: or X ft = 39.37 in = Again, the units must cancel.

  11. 1 km 1,000 m ( ) ______ ( ) ____ 1 m 10 dm 1.5 km How many kilometers is 15,000 decimeters? X km = 15,000 dm =

  12. ( ) _____ 60 min 1 h 378,432 s ( ) ( ) ____ 60 s 3.78 x 105 s ____ 24 h 1 min 1 d How many seconds is 4.38 days? X s = 4.38 d = If we are accounting for significant figures, we would change this to…

  13. Simple MathwithConversion Factors

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

  15. ( ( ( ( ) ) ) ) ______ ______ ______ ______ 1 m 1 m 1 m 1 m 100 cm 100 cm 100 cm 100 cm 2 X m2 = 41.2 cm2 = 0.412 m2 WRONG! Convert 41.2 cm2 to m2. = 0.412 cm.m Recall that… 41.2 cm2 = 41.2 cm.cm X m2 = 41.2 cm.cm = 0.00412 m2 X m2 = 41.2 cm2 = 0.00412 m2

  16. 10 mm 10 mm 10 mm 1 cm 1 cm 1 cm ( ( ( ) ) ) _____ _____ _____ 2 Convert 41.2 cm2 to mm2. Recall that… 41.2 cm2 = 41.2 cm.cm X mm2 = 41.2 cm.cm = 4,120 mm2 X mm2 = 41.2 cm2 = 4,120 mm2

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

  18. ( ( ( ( ) ) ) ) 1 m 1 m 1 m 1 m _____ _____ _____ _____ 100 cm 100 cm 100 cm 100 cm ( ) 3 1 m _________ 3 1000000 cm cm.cm.cm 2 3 X m3 = 480 cm Convert to m3. = or 3 X m3 = 480 cm3 = 0.000480 m3 or 4.80 x 10-4 m3 X m3 = 480 cm3 =

  19. Convert to m3... Measured dimensions of a rectangular solid: Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm 0.152 m 0.037 m 0.086 m H W Find volume of solid. L V = L . W . H = (0.152 m)(0.037 m)(0.086 m) m = 0.000480 3

  20. Convert to mm3.

  21. By what factor do mm and cm differ? 10 By what factor do mm2 and cm2 differ? 100 By what factor do mm3 and cm3 differ? 1,000 1 cm = 10 mm 1 cm2 = 100 mm2 (1 cm)2 = (10 mm)2 1 cm3 = 1000 mm3 (1 cm)3 = (10 mm)3

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