Conversion Factors and Unit Cancellation

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Conversion FactorsandUnit Cancellation
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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
(
)
(
)
36 inches
3 feet
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
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.
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• How many meters is 8.72 cm?

equality
1 m 100 cm
applicable conversion factors
or
X m 8.72 cm

Again, the units must cancel.
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• How many feet is 39.37 inches?

equality
1 ft 12 in
applicable conversion factors
or
X ft 39.37 in

Again, the units must cancel.
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• How many kilometers is 15,000 decimeters?

X km 15,000 dm

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How many seconds is 4.38 days?
X s 4.38 d

If we are accounting for significant figures, we
would change this to
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Real Life Chemistry
Real Life Chemistry
Real Life Chemistry
Keys
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Simple MathwithConversion Factors
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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
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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

0.00412 m2
X m2 41.2 cm2

0.00412 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

4,120 mm2
X mm2 41.2 cm2

4,120 mm2
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• Measured dimensions of a rectangular solid

Length 15.2 cm Width 3.7 cm Height
8.6 cm
H
W
Find volume of solid.
L
V L . W . H
(15.2 cm)(3.7 cm)(8.6 cm)

480
cm
3
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• Convert to m3.

cm.cm.cm
2
3
X m3 480
cm

or
3
X m3 480 cm3

0.000480 m3
or
4.80 x 10-4 m3
X m3 480 cm3

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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
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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 cm2 100 mm2
(1 cm)2 (10 mm)2
(1 cm)3 (10 mm)3
1 cm3 1000 mm3
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Conversion Factors
Conversion Factors
Conversion Factors
Keys
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