Section 3A Uses and Abuses of Percentages

1. Section 3AUses and Abuses of Percentages Pages 135-154

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

3. 3-A To convert a percentage to a decimal simply divide by 100 or move the decimal two places to the left 45% = 45/100 = .45 1.2% = 1.2/100 = .012 To convert a decimal to a percentage simply multiply by 100% (=1) or move the decimal two places to the right: .16 = .16 * 100% = 16% 2.3 = 2.3 * 100% = 230%

4. 3-A 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 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%

5. 3-A 3 Ways of Using Percentages • As fractions and “Percent of” • To describe change over time • For comparison

6. 3-A 1. Percent “of “ - (multiply) 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 = 470 people

7. 3-A More Practice 55/151220 men at a conference of 430 people. Men are ____ percent of the conference participants.

8. 3-A 2. Percents are often used to describe how a quantity changes over time Given: original value and new value absolute change = new value – original value relative change

9. 3-A Absolute Change vs. Relative Change 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.

10. 3-A Absolute Change vs. Relative Change ex4/139A 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% ofthe value in 2003.]

11. 3-A Absolute Change vs. Relative Change ex2/138During 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% ofthe value yesterday.] What if my stock tripled in value?

12. 3-A Percentage Of vs. More (or Less) Than(page 142) 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. Practice: 73/152 and 75/132

13. 3-A 3. Percents are often used to compare two values. Given:comparedvalue andreferencevalue absolute difference = compared value  ‘reference’ value

14. 3-A 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 USA Today has 650,000 more readers than the NYT. Relative difference = 650000/1120000 = .580 = 58% USA Today has 58% more readers than the NYT.

15. 3-A Homework Pages 151 # 58, 63, 66, 70Express your answers in sentence form.