How to Factor Label 1 Factor Label 1.1

How to Factor Label
1
Factor Label
1.1
What is a conversion factor?
• Start with true statement
1 in. = 2.54 cm
• Let’s multiply by one
1 in. = 2.54 cm × 1 in.
• Reorganize
1 in.
2.54 cm
1 in. = 1 in.
• Simplify 1
1=
1 in.
2.54 cm
1 in.
←− conversion factor
Def : a conversion factor is always equal to one
Note: Units cancel out just like numbers and algebraic symbols
Examples:
1.2
cm2
= cm
cm
mL · g
= mL
g
How to Factor Label by Example
Problem: Convert 30 cm to inches.
1. Start with given
30 cm
2. Multiply by conversion factor 2,3
30.0 cm ×
3. Cancel units
×
30.0 cm
1 in.
cm
2.54 4. Solve 4
×
30.0 cm
1 in.
= 11.8 in.
2.54 cm
5. Box answer
×
30.0 cm
1 in.
= 11.8 in.
cm
2.54 1 in.
2.54 cm
• When converting units using the factor label method, the rules you applied for significant figures still
apply. You must always provide the correct number of significant figures as well as the correct unit.
1
It is a good exercise to work out solved examples with a pencil and paper to really understand every step.
As we saw earlier, we can do this because this is the same as multiplying by 1.
3
You insert the conversion factor into the equation so that undesired units cancel out leaving only the desired
ones. It is acceptable and often times necessary to inverse the conversion factor. Again, you can do this because the
conversation factor is equal to 1.
4
Your answer will be in inches because inches is the only unit left after cancellation.
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Length and Displacement Conversion Worksheet
Memorize:
Conversion factors in bold print are
exact and thus have an infinite number of significant figures.
mi. = 1.609 km
in. = 2.54 cm
mi. = 5 280 ft.
yd. = 36 in.
ft. = 12 in.
yd. = 3 ft.
Directions Convert the following using the factor label method and box your final answer. Your
answer must contain the correct number of significant figure and the proper unit. No unit should
be written out; use symbol only.
1
235 feet to inches
2
47.0 miles to feet
3
12 feet to centimeters
4
5.00 kilometers to miles
5
1.00 millimeter to inches
6
70¯0 inches to micrometers
7
100. miles to meters
8
1.0 angstrom to inches
2
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4.56×106 miles to gigameters
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0.531 miles to megameters
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2.0 exometers to miles
12
15.0 femtometers to inches
13
4.22 light years to miles
14
902 micrometers to inches
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0.020 miles to decimeters
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4.04×104 attometers to inches
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7¯00 meters to yards
18
10.0 feet to nanometers
3
Mass and Weight Conversion Worksheet
Memorize:
lb. = 453.6 g
ton = 2 000 lb.
lb. = 16 oz.
kg = 9.8 N 1
slug = 32.2 lb. 2
Conversion factors in bold print are
exact and thus have an infinite number of significant figures.
Directions Convert the following using the factor label method and box your final answer. Your
answer must contain the correct number of significant figure and the proper unit. No unit should
be written out; use symbol only.
19
5.00 pounds to kilograms
20
1.00 ounce to pounds
21
3.02 grams to ounces
22
60¯0 micrograms to pounds
23
2.000 tons to metric tons
24
5.21×107 femtograms to pounds
25
9.1093897×10−27 kilograms to ounces
1
2
Varies with distance above or below the earth’s surface.
Varies with distance above or below the earth’s surface.
4
26
100. newtons to pounds
27
145 pounds to slugs
28
12.000 atomic mass units to grams
29
60.0 kilograms to newtons
30
1.00797 grams to atomic mass units
31
0.045 decagrams to pounds
32
6.02×10−3 ton to newtons
33
2.20 slugs to teragrams
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18.01 ounces to pounds
35
mass of the earth in kilograms to pounds
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0.0310 newtons to grams
5
Volume Conversion Worksheet
Memorize:
L = 1.057 qt.
ft.3 = 28.32 L
gal. = 4 qt.
2 pt. = qt.
2 cups = pt.
cup = 8 fluid oz. 1
cm3 = mL
m3 = kL
ft.3 = (12 in.)3
in.3 = (2.54 cm)3
Conversion factors in bold
print are exact and thus have
an infinite number of significant figures.
Directions Convert the following using the factor label method and box your final answer. Your
answer must contain the correct number of significant figure and the proper unit. No unit should
be written out; use symbol only.
37
5.00 pounds to kilograms
38
22 cubic centimeters to liters
39
54.5 gallons to cups
40
1¯00 milliliters to cubic feet
41
1.9×1020 attoliters to pints
42
40.0 liters to cubic feet
43
0.0250 decaliters to cubic inches
1
A fluid ounce is a volume. An ounce is a weight.
6
44
700 cubic feet to microliters
45
60.0 cubic inches to cubic yards
46
45.0 cubic feet to milliliters
47
4.0 pt. to cubic centimeters
48
11.34 grams per milliliter to pounds per cubic inch
49
1.00 grams per milliliter to pounds per cubic foot
50
50¯0 tons per year to ounces per millisecond
51
60 miles per hour to kilometers per hour
52
25 meters per second to miles per hour
53
10. meters per second per second to feet per second per second
54
9.80 meters per second per second to feet per hour per second
7
Assorted Unit Conversion Worksheet
Directions Convert the following using the factor label method and box your final answer. Your
answer must contain the correct number of significant figure and the proper unit. No unit should
be written out; use symbol only.
55
18.0 km to mi.
(Ans. 11.2 mi.)
56
45 mi. to cm
57
650 g to lb.
58
42 tons to kg
59
16 L to qt.
60
100. gal to mL
61
75 km/h to m · s−1
62
194 kg/yr. to lb./day
63
815 in.2 to ft.2
(Ans. 7.2×106 cm)
(Ans. 1.4 lb.)
(Ans. 3.8×104 kg)
(Ans. 17 qt.)
(Ans. 3.77×105 mL)
Ans. 21 m · s−1 )
(Ans. 1.16 lb./day)
(Ans. 5.66 ft.2 )
8
64
32 yd.3 to in.3
(Ans. 1.5×106 in.3 )
65
16 ft.3 to cm2
(Ans. 1.5×104 cm2 )
66
200 cm3 to mL
67
6.3×109 TL to gal. (Ans. 1.7×1021 gal.)
68
6.5×104 cm to km. (Ans. 0.65 km)
69
15 EL to aL
70
(Ans. 200 mL)
(Ans. 1.5×1037 aL)
From here on out do not provide answers and use all sorts of units. (Continue using Mrs.
Crapps sheets.
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