Section 3A Uses and Abuses of Percentages

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Section 3AUses and Abuses of Percentages

• Pages 133-147

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Where do we use percents?
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Percents - A brief review
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per cent per 100 divided by
100

• 47 47/100 .47
• 2 2/100 .02
• 813 813/100 8.13
• To divide by 100, move the decimal 2 places to
  the left.

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To convert a percentage to a fraction

• Divide by 100
• 45 45/100 9/20
• 2 2/100 1/50
• 525 525/100 21/4

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To convert a percentage to a decimal

• Divide by 100 and write as a decimal (so move
  the decimal 2 places to the left)
• 45 45/100 .45
• 2 2/100 .02
• 525 525/100 5.25

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To convert a decimal to a percentage

• Multiply by 100 and add the symbol (so move
  the decimal 2 places to the right)
• .38 100 ? .38 38
• .075 100 ? .075 7.5
• 1.98 100 ? 1.98 198

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3 Ways of Using Percentages

1. As fractions Percent of
2. To describe change over time
3. For comparison

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1. Percent of -gt multiply

• In 2000, 14.4 of the citizens in Alabama lived
  in poverty. The population of Alabama was
  642,000. How many people were living in poverty?
• (14.4 ) ? (642,000)
• (.144) ? (642,000)
• 92,448 people

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2. Percents are often used to describe how a
quantity changes over time
3-A
Absolute Change vs. Relative Change
Example A diversified portfolio grows from
1,500 to 2,250.
absolute change
new value original value
2,250 1,500 750
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Absolute Change vs. Relative Change
3-A
Example A diversified portfolio grows from
1,500 to 2,250.
relative change
750 / 1,500 .50 50

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During the last year, my stock doubled in price
from 3500 to 7000.

• Absolute change in price 7000-3500
• 3500
• Relative change in price

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Suppose my stock tripled in price from 3500 to
10,500.

• Absolute change in price 10,500-3500
• 7000
• Relative change in price

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3. Percentages Used for Comparisons

• Compare the value/quantity of two different items
• As with change we can compare Absolutely
  or
• Relatively (as a percent)
• Pick one value to compare to this is your
  reference value

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Absolute and Relative Difference
3-A

• The absolute difference is the actual difference
  between the compared value and the reference
  value
• absolute difference compared value ?
  reference value
• The relative difference describes the size of the
  absolute difference as a fraction of the
  reference value

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• Daily circulation of the Wall Street Journal
  1.77 million
• Daily circulation of the New York Times is 1.07
  million
• Compare the circulation of the WSJ to the NYT.
• Reference value 1.07 million (NYT)
• Compared value 1.77 million (WSJ)

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• Compared value 1.77 million (WSJ)
• Reference value 1.07 million (NYT)
• Absolute difference compared-reference
• 1.77 million 1.07 million
• .7 million
• 700,000
• WSJ has about 700,000 more readers than the NYT.

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• Compared value 1.77 million (WSJ)
• Reference value 1.07 million (NYT)
• Relative difference (absolute difference)
• reference value
• (.7 million) / 1.07 million
• .654
• 65.4
• The Wall Street Journals circulation is about
  65.4 more than the New York Times.

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• Now,
• Compare the circulation of the NYT to the WSJ.
• Reference value 1.77 million (WSJ)
• Compared value 1.07 million (NYT)

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• Compared value 1.07 million (NYT)
• Reference value 1.77 million (WSJ)
• Absolute difference compared-reference
• 1.07 million 1.77 million
• -.7 million
• -700,000
• NYT has about 700,000 fewer readers than the WSJ.

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• Compared value 1.07 million (NYT)
• Reference value 1.77 million (WSJ)
• Relative difference (absolute difference)
• reference value
• (-.7 million) / 1.77 million
• -.396
• -39.6
• The New York Times circulation is about 39.6
  less than the Wall Street Journals.

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Solving Percentage Problems
3-A

• Example You purchase a shirt with a labeled
  (pre-tax) price of 21. The local sales tax rate
  is 6. What is your final cost?
• final cost
• 100 of labeled price 6 of
  labeled price
• (100 6) ? labeled price
• 106 ? 21 1.06 ? 21
  
• 22.26

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3-A

• Example Your receipt shows that you paid 19.35
  for a DVD, tax included. The local sales tax
  rate is 7.5. What was the labeled (pre-tax)
  price of the DVD?
• final cost
• 100 labeled price 7.5 of labeled
  price
• (100 7.5) ? labeled price
• 19.35 107.5 ? labeled price
  
• 19.35 / 1.075 labeled price
• 18.00

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• Homework for Friday
• Pages 147-150
• 11, 28, 30, 46, 52, 56, 62, 78, 82