Section 3AUses and Abuses of Percentages

Pages 135-154

per cent = “per 100” = “divided by 100”

47% = 47/100 = .47

2% = 2/100 = .02

813% = 813/100 = 8.13

percentage fraction decimal

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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 To convert a decimal to a percentage simply simply multiply by 100% (=1) or move the decimal multiply by 100% (=1) or move the decimal two places to the right: 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%

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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 To convert a fraction to a percentage simply simply divide to get a decimal and then move divide to get a decimal and then move decimal two spaces to the right:decimal two spaces to the right:

1/5 = .20 = .20 * 100% = 20%

5/4 = 1.25 = 1.25*100% = 125%

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3 Ways of Using Percentages

1. As fractions and “Percent of”

2. To describe change over time

3. For comparison

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1. Percent “of “ - (multiply)

ex1/134 A newspaper reports that 44% of 1069 A newspaper reports that 44% of 1069 people surveyed said that the president was doing a people surveyed said that the president was doing a good job. How many people said this? good job. How many people said this?

44% * 1069 = .44*1069 = 470.36 = 44% * 1069 = .44*1069 = 470.36 = 470 people

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More Practice

55/151220 men at a conference of 430 people.

Men are ____ percent of the conference participants.

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2. Percents are often used to describe how a quantity changes

over time

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absolute change = new value – original value

Given: original value and new value

relative change

absolute change= original value

new value original value= original value

Absolute Change vs. Relative Change

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61/151 John’s salary grew from $20,000 in 2000 to $28,000 in 2003. 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 Mary’s salary grew from $25,000 to $35,000 in the same period. Whose salary grew more in absolute terms? relative terms?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.

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.]

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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?

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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)

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Practice: 73/152 and 75/132

3. Percents are often used to compare two values.

Given: compared value and reference value

absolute differencerelative difference =

reference value

compared value reference value

reference value

absolute difference = compared value ‘reference’ value

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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.

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Homework

Pages 151

# 58, 63, 66, 70

Express your answers in sentence form.

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