# Conversion Factors and Unit Cancellation - Sayre School 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 12 inches

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

Calculation Corner: Unit Conversion 1 foot 12 inches 12 inches 1 foot Conversion factors Calculation Corner: Unit Conversion 1 foot 12 inches 12 inches 1 foot

Conversion factors ( 3 feet )( 12 inches 1 foot ) = 36 inches How many cm are in 1.32 meters? equality: 1 m = 100 cm (or 0.01 m = 1 cm)

applicable conversion factors: ______ 1m 100 cm or ( 100 cm ______ 1m ) 100 cm = 132 cm X cm = 1.32 m ______ 1m We use the idea of unit cancellation to decide upon which one of the two

conversion factors we choose. How many meters is 8.72 cm? equality: 1 m = 100 cm applicable conversion factors: ______ 1m 100 cm or ( 100 cm ______ 1m ) 1m

X m = 8.72 cm ______ = 0.0872 m 100 cm Again, the units must cancel. How many feet is 39.37 inches? equality: 1 ft = 12 in applicable conversion factors: ______ 1 ft 12 in or ( ) 1 ft X ft = 39.37 in ____ 12 in

______ 12 in 1 ft = 3.28 ft Again, the units must cancel. How many kilometers is 15,000 decimeters? ( )( 1m X km = 15,000 dm ____ 10 dm ) 1 km ______

= 1.5 km 1,000 m How many seconds is 4.38 days? ( )( 24 h X s = 4.38 d ____ 1d )( ) 60 min _____ 1h 60 s

____ 1 min = 378,432 s If we are accounting for significant figures, we would change this to 3.78 x 105 s Simple Math with Conversion Factors Example Problem Measured dimensions of a rectangle: length (L) = 9.70 cm width (W) = 4.25 cm Find area of rectangle. A=L.W

L = (9.70 cm)(4.25 cm) = 41.2 cm2. cm W Convert 41.2 cm2 to m2. ( ) 1m X m2 = 41.2 cm2 ______ = 0.412 m2 WRONG! 100 cm = 0.412 cm.m Recall that

41.2 cm2 = 41.2 cm.cm X m2 = 41.2 cm.cm ( )( 1m ______ 100 cm ) 1m ______ 100 cm = 0.00412 m2

( ) 1m X m2 = 41.2 cm2 ______ 100 cm 2 = 0.00412 m2 Convert 41.2 cm2 to mm2. Recall that 41.2 cm2 = 41.2 cm.cm

( X mm2 = 41.2 cm.cm 10 mm _____ 1 cm )( 10 mm _____ 1 cm ) = 4,120 mm2 X mm = 41.2 cm 2

2 ( 10 mm _____ 1 cm ) 2 = 4,120 mm2 Measured dimensions of a rectangular solid: Length = 15.2 cm Width = 3.7 cm

Height = 8.6 cm Find volume of solid. H L V=L.W.H = (15.2 cm)(3.7 cm)(8.6 cm) = 480 cm3 W Convert to m3. cm.cm.cm ( )( (

) 1m X m3 = 480 cm32 _____ 100 cm 1m _____ )( 100 cm ) 1m _____ = 100 cm

or X m = 480 cm 3 3 1m _____ 100 cm 3 = 0.000480 m3 or

X m = 480 cm 3 3 ( 3 ) 1m _________ 4.80 x 10-4 m3 = 3 1000000 cm Convert to m3...

Measured dimensions of a rectangular solid: Length = 15.2 cm 0.152 m Width = 3.7 cm 0.037 m Height = 8.6 cm 0.086 m H Find volume of solid. L V=L.W.H = (0.152 m)(0.037 m)(0.086 m) = 0.000480 m3 W Convert to mm3. By what factor do mm and cm differ? 10 1 cm = 10 mm

By what factor do mm2 and cm2 differ? 100 1 cm (1 cm)22==100 (10 mm mm)2 2 By what factor do mm3 and cm3 differ? 1,000 1 cm mm33 (1 cm)3 3==1000 (10 mm)