Section 5.3 Percents

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Section 5.3 Percents

• Percent means "for every 100."
• The unemployment of 5 means that 5 out of every
  100 people are unemployed.
• An increase in tuition of 10 means that tuition
  has gone up 10 for every 100 it cost previously.

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• A percent is a ratio of a number to 100.
• Thus 1 1/1000.01
• 17 17(1) 17(0.01) 0.17
• 0.17 17(0.01) 17(1) 17

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• EXAMPLE 1.Write the percent as a decimal.
• a. 24 b. 183 c. 6.5 d.0.9
• CHECK YOUR PROGRESS 1 Write the percent as a
  decimal
• a. 74 b. 152 c.8.3 d. 0.6.

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• EXAMPLE 2 . Write a Decimal as a Percent
• a. 0.62 b. 1.5 c. 0.059 d. 0.008
• CHECK YOUR PROGRESS 2 Write the decimal as a
  percent.
• a. 0.3 b. 1.65 c. 0.072 d. 0.004

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• EXAMPLE 3. Write the percent as a fraction.
• a. 25 b. 120 c. 7.5 d. 33 1/3
• CHECK YOUR PROGRESS 3
• Write the percent as a fraction.
• a. 8 b. 180 c.2.5 d. 66 2/3

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• EXAMPLE 4 Write the fraction as a percent.
• a. ¾ b. 5/8 c 1/6 d. 3/2.

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• The Proportion Used to Solve Percent Problems
• Percent/100 amount / base
• EXAMPLE 5 The average size of a house in 1997 was
  2100 square feet. This is approximately 125 of
  the average size of a house in 1977. What was the
  average size of a house in 1977?
• CHECK YOUR PROGRESS 5 A used Chevrolet Blazer
  was purchased for 22,400. This was 70 of the
  cost of the Blazer when new. What was the cost of
  the Blazer when it was new?

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• EXAMPLE 6 During 1996, Texas suffered through
  one of its longest droughts in history. Of the 5
  billion in losses caused by the drought, 1.1
  billion was direct losses to ranchers. What
  percent of the total losses was direct losses to
  ranchers?
• CHECK YOUR PROGRESS 7
• A General Motors buyers' incentive program
  offered a 3.5 rebate on the selling price of a
  new car. What rebate would a customer receive who
  purchased a 32,500 car under this program?

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• EXAMPLE 8. A real estate broker receives a
  commission of 6 of the selling price of a house.
  Find the amount the broker receives on the sale
  of a 175,000 home.
• CHECK YOUR PROGRESS 8
• New Hampshire public school teachers contribute
  5 of their wages to the New Hampshire Retirement
  System. What amount is contributed during one
  year by a teacher whose annual salary is 32,685?

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• EXAMPLE 9 An investor received a payment of 480,
  which was 12 of the value of the investment.
  Find the value of the investment.
• CHECK YOUR PROGRESS 9 A real estate broker
  receives a commission of 6 of the selling price
  of a house. Find the selling price of a home on
  whose sale the broker received a commission of
  14,370.

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• EXAMPLE 10. If you answer 96 questions correctly
  on a 120-question exam, what percent of the
  questions did you answer correctly?
• CHECK YOUR PROGRESS 10
• If you answer 63 questions correctly on
  90-question exam, what percent of the questions
  did you answer correctly?