# Section 3Af2008pI by xiagong0815

VIEWS: 1 PAGES: 15

• pg 1
```									          Section 3A
Uses and Abuses of Percentages
Pages 135-154
3-A

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

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

percentage   fraction   decimal
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%
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%
3-A

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

More Practice

55/151
220 men at a conference of 430 people.
Men are ____ percent of the
conference participants.
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   = absolute change
original value

= new value  original value
original value
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.
3-A

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

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

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
3-A

3. Percents are often used to compare
two values.
Given: compared value and reference value

absolute difference = compared value  ‘reference’ value

absolute difference
relative difference =
reference value

compared value  reference value

reference value
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.
3-A

Homework

Pages 151
# 58, 63, 66, 70