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
= 1
12 inches
1 foot
= 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?
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)
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
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
How many kilometers is 15,000 decimeters?
X km = 15,000 dm
=
1.5 km
(
)
____
1,000 m
1 km
10 dm
1 m
(
)
______
How many seconds is 4.38 days?
=
1 h
60 min
24 h
1 d
1 min
60 s
____
(
)
(
)
____
(
)
_____
X s = 4.38 d
378,432 s
3.78 x 105 s
If we are accounting for significant figures, we would change this to…
Real Life Chemistry
Keys
Real Life Chemistry
Real Life Chemistry
http://www.unit5.org/chemistry/intro.html
Simple Math�with�Conversion Factors
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
cm
2
. cm
Convert 41.2 cm2 to m2.
100 cm
1 m
(
)
______
X m2 = 41.2 cm2
X m2 = 41.2 cm.cm
Recall that… 41.2 cm2 = 41.2 cm.cm
100 cm
1 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
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
(
)
_____
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
cm
3
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 m
1000000 cm
(
)
_________
3
3
4.80 x 10-4 m3
or
3
2
cm
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 m3...
Convert to mm3.
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)2
1 cm2 = 100 mm2
(1 cm)3 = (10 mm)3
1 cm3 = 1000 mm3
Conversion Factors
Keys
Conversion Factors
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