Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.
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Transcript of Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.
![Page 1: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/1.jpg)
Conversion Factorsand
Unit Cancellation
![Page 2: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/2.jpg)
A physical quantity must include:A physical quantity must include:
NumberNumber + Unit+ Unit
![Page 3: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/3.jpg)
Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion
1 foot = 12 inches1 foot = 12 inches
![Page 4: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/4.jpg)
Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion
1 foot = 12 inches1 foot = 12 inches
1 foot1 foot
12 inches12 inches= 1= 1
![Page 5: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/5.jpg)
Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion
1 foot = 12 inches1 foot = 12 inches
1 foot1 foot
12 inches12 inches= 1= 1
12 inches12 inches
1 foot1 foot= 1= 1
![Page 6: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/6.jpg)
Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion
1 foot1 foot
12 inches12 inches
12 inches12 inches
1 foot1 foot
“Conversion factors”“Conversion factors”
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Calculation Corner: Unit ConversionCalculation Corner: Unit Conversion
1 foot1 foot
12 inches12 inches
12 inches12 inches
1 foot1 foot
“Conversion factors”“Conversion factors”
3 feet3 feet12 inches12 inches
1 foot1 foot= 36 inches= 36 inches(( ))(( ))
![Page 8: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/8.jpg)
How many cm are in 1.32 meters?
applicable conversion factors:
equality:
or
X cm = 1.32 m =
1 m = 100 cm
______1 m100 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)
![Page 9: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/9.jpg)
How many meters is 8.72 cm?
applicable conversion factors:
equality:
or
X m = 8.72 cm =
1 m = 100 cm
______1 m100 cm
Again, the units must cancel.
______1 m
100 cm
( )______ 0.0872 m1 m100 cm
![Page 10: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/10.jpg)
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 ft1 ft12 in
______1 ft
12 in
![Page 11: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/11.jpg)
How many kilometers is 15,000 decimeters?
X km = 15,000 dm = 1.5 km( )____1,000 m
1 km10 dm
1 m ( )______
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How many seconds is 4.38 days?
=
1 h60 min24 h
1 d 1 min60 s____( ) ( )____( )_____X s = 4.38 d
378,432 s
3.78 x 105 sIf we are accounting for significant figures, we would change this to…
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Simple Mathwith
Conversion Factors
![Page 14: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/14.jpg)
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
41.2 cm2 . cm
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Convert 41.2 cm2 to m2.
100 cm1 m( )______
X m2 = 41.2 cm2
X m2 = 41.2 cm.cm
Recall that… 41.2 cm2 = 41.2 cm.cm
100 cm1 m( )______
X m2 = 41.2 cm2 = 0.412 m2
= 0.412 cm.m
WRONG!
( )______100 cm
1 m
= 0.00412 m2
( )______100 cm
1 m 2 = 0.00412 m2
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Convert 41.2 cm2 to mm2.
X mm2 = 41.2 cm2
X mm2 = 41.2 cm.cm
Recall that… 41.2 cm2 = 41.2 cm.cm
1 cm
10 mm( )_____
= 4,120 mm2
=
1 cm
10 mm( )_____
4,120 mm2
1 cm
10 mm 2( )_____
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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)
= 480 cm3
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Convert to m3.
X m3 = 480 cm3 = 0.000480 m3
100 cm
1 m 3
( )_____
X m3 = 480 cm3 =
X m3 = 480
100 cm
1 m( )_____100 cm
1 m( )_____100 cm
1 m( )_____ =
or
cm.cm.cm
1 m1000000 cm( )_________
3
34.80 x 10-4 m3
or
32cm
![Page 19: Conversion Factors and Unit Cancellation A physical quantity must include: Number + Unit + Unit.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d875503460f94a6c47c/html5/thumbnails/19.jpg)
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 m3
0.152 m0.037 m
0.086 m
Convert to m3...
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Convert to mm3.
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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 cm)2 = (10 mm)21 cm2 = 100 mm2
(1 cm)3 = (10 mm)31 cm3 = 1000 mm3