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Section 3A Uses and Abuses of Percentages Pages 135-154

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per cent = “per 100” = “divided by 100” 47% = 47/100 =.47 2% = 2/100 =.02 813% = 813/100 = 8.13 percentage fractiondecimal 3-A

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To convert a percentage to a decimal simply divide by 100 or move the decimal two places to the left To convert a simply multiply by 100% (=1) or move the decimal two places to the right: To convert a decimal to a percentage simply multiply by 100% (=1) or move the decimal two places to the right: 45% = 45/100 =.45 1.2% = 1.2/100 =.012.16 =.16 * 100% = 16% 2.3 = 2.3 * 100% = 230% 3-A

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To convert a percentage to a fraction simply divide by 100 and reduce as necessary: 45% = 45/100 = 9/20 1.2% = 1.2/100 = 12/1000 = 3/250 To convert a simply divide to get a decimal and then move decimal two spaces to the right: To convert a fraction to a percentage simply divide to get a decimal and then move decimal two spaces to the right: 1/5 =.20 =.20 * 100% = 20% 5/4 = 1.25 = 1.25*100% = 125% 3-A

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3 Ways of Using Percentages 1. As fractions and “Percent of” 2. To describe change over time 3. For comparison 3-A

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1. Percent “of “ - (multiply) A newspaper reports that 44% of 1069 people surveyed said that the president was doing a good job. How many people said this? ex1/134 A newspaper reports that 44% of 1069 people surveyed said that the president was doing a good job. How many people said this? 44% * 1069 =.44*1069 = 470.36 = 44% * 1069 =.44*1069 = 470.36 = 470 people 3-A

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More Practice 55/151 220 men at a conference of 430 people. Men are ____ percent of the conference participants. 3-A

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2. Percents are often used to describe how a quantity changes over time 3-A absolute change= new value – original value Given: original value and new value relative change

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Absolute Change vs. Relative Change 3-A John’s salary grew from $20,000 in 2000 to $28,000 in 2003. Mary’s salary grew from $25,000 to $35,000 in the same period. Whose salary grew more in absolute terms? relative terms? 61/151 John’s salary grew from $20,000 in 2000 to $28,000 in 2003. Mary’s salary grew from $25,000 to $35,000 in the same period. Whose salary grew more in absolute terms? relative terms? John’s absolute change = $28000 – $20000 = $8000 John’s relative change = $8000/$20000 =.40 = 40% John’s salary in 2003 was 40% more than his salary in 2000 Mary’s absolute change = $35000 – $25000 = $10000 Mary’s relative change = $10000/$25000 =.40 = 40% Mary’s salary in 2003 was 40% more than her salary in 2000. [John’s 2003 salary is 28000/20000 = 1.40 = 140% of his 2000 salary.

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Absolute Change vs. Relative Change ex4/139 A computer you bought three years ago for $1000 is today worth only $300. absolute change = $300 – $1000 = -$700 relative change = -$700/$1000 = -.70 = -70% The value of the computer today is 70% less than its value three years ago. [The computer’s value today is 300/1000 =.30 = 30% of the value in 2003.] 3-A

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Absolute Change vs. Relative Change ex2/138 During a 6-month period, Nokia’s stock doubled in price from $10 to $20. absolute change = $20 – $10 = $10 relative change = $10/$10 = 1 = 100% The value of stock today is 100% more than yesterday’s value. [The stock’s value today is 20/10 = 2 = 200% of the value yesterday.] What if my stock tripled in value? 3-A

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If the new value is P% more than the original value, then the new value is (100+P)% of the original value. If the new value is P% less than the original value, then the new value is (100-P)% of the original value. Percentage Of vs. More (or Less) Than (page 142) 3-A Practice: 73/152 and 75/132

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3. Percents are often used to compare two values. Given: compared value and reference value absolute difference = compared value ‘reference’ value 3-A

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67*/149 The daily circulation of USA Today is ≈ 1.77 million. The daily circulation of the New York Times is ≈ 1.12 million [Find the absolute and relative difference. Assume that the first quantity is the compared value and the second is the reference value.] Absolute difference = 1770000-1120000=650000 Relative difference = 650000/1120000 =.580 = 58% USA Today has 650,000 more readers than the NYT. USA Today has 58% more readers than the NYT. 3-A

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Homework Pages 151 # 58, 63, 66, 70 Express your answers in sentence form. 3-A

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