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Section 3A Uses and Abuses of Percentages

Section 3A Uses and Abuses of Percentages. Pages 133-147. Where do we use percents?. Percents - A brief review. per cent = “per 100” = “divided by 100”. 47% = 47/100 = .47 2% = 2/100 = .02 813% = 813/100 = 8.13

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Section 3A Uses and Abuses of Percentages

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  1. Section 3AUses and Abuses of Percentages Pages 133-147

  2. Where do we use percents?

  3. Percents - A brief review

  4. 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.

  5. 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

  6. 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

  7. 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%

  8. 3 Ways of Using Percentages • As fractions – “Percent of” • To describe change over time • For comparison

  9. 1. Percent “of “ -> 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

  10. 3-A 2. Percents are often used to describe how a quantity changes over time 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

  11. 3-A Absolute Change vs. Relative Change Example: A diversified portfolio grows from $1,500 to $2,250. relative change = $750 / $1,500 = .50 = 50%

  12. During the last year, my stock doubled in price from $3500 to $7000. • Absolute change in price = $7000-$3500 = $3500 • Relative change in price =

  13. Suppose my stock tripled in price from $3500 to $10,500. • Absolute change in price = $10,500-$3500 = $7000 • Relative change in price =

  14. 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”

  15. 3-A Absolute and Relative Difference 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:

  16. 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)

  17. 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.

  18. 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 Journal’s circulation is about 65.4% more than the New York Times’.

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

  20. 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.

  21. 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 Journal’s.

  22. 3-A Solving Percentage Problems 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

  23. 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

  24. Homework for Friday: Pages 147-150 # 11, 28, 30, 46, 52, 56, 62, 78, 82

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