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Conversion Factors and Unit Cancellation
Converting between two sets of units never changes the number of significant figures in a measurement. Remember, data are only as good as the original measurement, and no later manipulations can clean them up.
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A physical quantity must include:
Number + Unit
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Calculation Corner: Unit Conversion
1 foot = 12 inches
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Calculation Corner: Unit Conversion
1 foot = 12 inches 1 foot = 1 12 inches
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Calculation Corner: Unit Conversion
1 foot = 12 inches 1 foot = 1 12 inches 12 inches = 1 1 foot
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Calculation Corner: Unit Conversion
1 foot 12 inches 12 inches 1 foot “Conversion factors”
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Calculation Corner: Unit Conversion
1 foot 12 inches 12 inches 1 foot “Conversion factors” 12 inches ( ) ( ) 3 feet = 36 inches 1 foot
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( ) ______ How many cm are in 1.32 meters? equality: 1 m = 100 cm
(or 0.01 m = 1 cm) applicable conversion factors: ______ 1 m 100 cm ______ 1 m 100 cm or ( ) ______ 1 m 100 cm 132 cm X cm = 1.32 m = We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose.
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Again, the units must cancel.
How many meters is 8.72 cm? equality: 1 m = 100 cm applicable conversion factors: ______ 1 m 100 cm ______ 1 m 100 cm or ( ) ______ 1 m 100 cm m X m = 8.72 cm = Again, the units must cancel.
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Again, the units must cancel.
How many feet is inches? equality: 1 ft = 12 in applicable conversion factors: ______ 1 ft 12 in ______ 1 ft 12 in or ( ) ____ 1 ft 12 in 3.28 ft X ft = in = Again, the units must cancel.
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( ) ( ) _____ ______ How many kilometers is 15,000 decimeters? 10 dm
1x10-1m 1x103 m 1 km 1.5 km x km = 15,000 dm =
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How many seconds is 4.38 days?
____ ( ) ( ) _____ ( ) ____ 24 h 1 d 1 h 60 min 1 min 60 s X s = 4.38 d 378,432 s = If we are accounting for significant figures, we would change this to… 3.78 x 105 s
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Example Problem Measured dimensions of a rectangle:
length (L) = 9.70 cm width (W) = 4.25 cm L W Find area of rectangle. A = L . W = (9.70 cm)(4.25 cm) = 41.2 cm 2 . cm
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( ) ( ) ( ) ( ) Convert 41.2 cm2 to m2. ______ ______ ______ ______
X m2 = 41.2 cm2 = 0.412 m2 WRONG! = 0.412 cm.m Recall that… 41.2 cm2 = 41.2 cm.cm ( ) ______ ( ) ______ X m2 = 41.2 cm.cm 100 cm 1 m 100 cm 1 m = m2 ( ) ______ 100 cm 1 m 2 X m2 = 41.2 cm2 = m2
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( ) ( ) ( ) Convert 41.2 cm2 to mm2. _____ _____ _____
Recall that… 41.2 cm2 = 41.2 cm.cm ( ) _____ ( ) _____ X mm2 = 41.2 cm.cm 1 cm 10 mm 1 cm 10 mm = 4,120 mm2 2 ( ) _____ 1 cm 10 mm X mm2 = 41.2 cm2 = 4,120 mm2
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