Section 3AUses and Abuses of Percentages

Pages 133-147

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

47% = 47/100 = .47 2% = 2/100 = .02 813% = 813/100 = 8.13

percentage fraction decimal/

proportion

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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),multiply by 100% (=1), or move the decimal two places to the right:or move the decimal two places to the right:

45% = 45/100 = .45

1.2% = 1.2/100 = .012

714% = 714/100 = 7.14

.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

1.3% = 1.3/100 = 13/1000

525% = 525/100 = 21/4To 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 – “Percent of”2. To describe change over time3. For comparison

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1. Percent “of “ - (multiply)

In 2004, 9.7% of the citizens in Virginia lived in poverty. The population of Virginia was 7,495,827. How many people in Virginia were living in poverty?

‘‘9.7% × 7,459,827’9.7% × 7,459,827’ = .097 × 7,459,827 = 727,095.219 = .097 × 7,459,827 = 727,095.219 = = 727,095 people

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More Practice

Suppose A is 75 and B is 480.

A is ____________ percent of B.

B is ____________ percent of A.

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75.15625,

480 So, A is 15.625% of B.

and B is 640% of A.4806.4,

75

More Practice

345 blooming tulips in a field of 398 tulips.

The blooming tulips are __??___ percent of the field.field.

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345.8668 86.7%

398

876 398 34. 5.066

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

over time

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Given: original value and new value

absolute change newvalue original value

absolutechangerelative change

original value

new value original value

original value

Absolute Change vs. Relative Change

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John’s salary grew from $20,000 in 2001 to John’s salary grew from $20,000 in 2001 to $28,000 in 2003.$28,000 in 2003.

absolute change = $28,000 – $20,000 = $8000relative change = $8000/$20,000 = .40 = 40%

John’s salary in 2003 was 40% more than his salary in 2001.

[John’s salary in 2003 was 28,000/20,000 = 1.40 = 140% of his salary in 2001.]

Absolute Change vs. Relative Change

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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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 140)

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Absolute Change vs. Relative Change

Today, my stock doubled in price from $1000 to $2000.

absolute change = $2000 – $1000 = $1000

relative change = $1000/$1000 = 1 = 100%

The value of stock today is 100% more than yesterday’s value. (Today’s price is 200% of yesterday’s price.)

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Absolute Change vs. Relative Change

How much would stock have to grow to in order to see a relative change of 200%?

absolute change = $2000 =$3000– $1000

relative change = 200% = 2 = $2000/$1000

So my stock had to triple in value.

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Homework

Pages 148-150# 22, 30, 50, 52, 56Express your answers in sentence

form.

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