III. Also called the Factor-Label Method for solving problems

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Dimensional Analysis

• III. Also called the Factor-Label Method for
  solving problems

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A. SI Prefix Conversions

• 1. Find the difference between the exponents of
  the two prefixes.
• 2. Move the decimal that many places.

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A. SI Prefix Conversions
0.532
532 m _______ km
NUMBER
UNIT
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A. SI Prefix Conversions
Prefix
Symbol
Factor
move left
move right
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A. SI Prefix Conversions
0.2

• 1) 20 cm ______________ m
• 2) 0.032 L ______________ mL
• 3) 45 ?m ______________ nm
• 4) 805 dm ______________ km

32
45,000
0.0805
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B. Dimensional Analysis

• The Factor-Label Method
• A method of using units (labels, dimensions) to
  analyze and solve word problems
• Cancel out units (dimensions)!

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B. Dimensional Analysis

• Steps
• Identify the final units of the answer
• (and necessary equalities)
• 2. Start by writing the given
• (magnitude and dimension)
• 3. Cancel units using conversion factor
  equalities
• (the numerator must equal denominator)
• 4. Multiply all top numbers divide by each
  bottom number.
• (calculate the numbers!)

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B. Dimensional Analysis

• Lining up conversion factors

1
1 in 2.54 cm
2.54 cm 2.54 cm
1
1 in 2.54 cm
1 in 1 in
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B. Dimensional Analysis

• How many milliliters are in 1.00 quart of milk?

1.00 qt
1 L 1.057 qt
1000 mL 1 L
946 mL
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B. Dimensional Analysis

• You have 1.5 pounds of gold. Find its volume in
  cm3 if the density of gold is 19.3 g/cm3.

1 cm3 19.3 g
1.5 lb
1 kg 2.2 lb
1000 g 1 kg
35 cm3
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B. Dimensional Analysis

• How many liters of water would fill a container
  that measures 75.0 in3?

75.0 in3
(2.54 cm)3 (1 in)3
1 L 1000 cm3
1.23 L
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B. Dimensional Analysis

• 5) Your European hairdresser wants to cut your
  hair 8.0 cm shorter. How many inches will he be
  cutting off?

8.0 cm
1 in 2.54 cm
3.2 in
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B. Dimensional Analysis

• 6) Taft football needs 550 cm for a 1st down.
  How many yards is this?

550 cm
1 in 2.54 cm
1 ft 12 in
1 yd 3 ft
6.0 yd
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B. Dimensional Analysis

• 7) A piece of wire is 1.3 m long. How many
  1.5-cm pieces can be cut from this wire?

1.3 m
100 cm 1 m
1 piece 1.5 cm
86 pieces