Section 3A Uses and Abuses of Percentages

1
Section 3AUses and Abuses of Percentages

• Pages 135-154

2
per cent per 100 divided by
100
3-A

• 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
1.25100 125
5
3 Ways of Using Percentages
3-A

• As fractions and Percent of
• To describe change over time
• For comparison

6
1. Percent of - (multiply)
3-A

• 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 .441069 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
2. Percents are often used to describe how a
quantity changes over time
3-A
Given original value and new value
absolute change
new value original value
relative change
9
Absolute Change vs. Relative Change
3-A
61/151 Johns salary grew from 20,000 in 2000
to 28,000 in 2003. Marys salary grew from
25,000 to 35,000 in the same period. Whose
salary grew more in absolute terms? relative
terms?
Johns absolute change 28000 20000 8000
Johns relative change 8000/20000 .40 40

Johns salary in 2003 was 40 more than his
salary in 2000
Marys absolute change 35000 25000
10000
Marys relative change 10000/25000 .40
40
Marys salary in 2003 was 40 more than her
salary in 2000.
Johns 2003 salary is 28000/20000 1.40 140
of his 2000 salary.
10
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 computers value today is 300/1000 .30
30 of the value in 2003.
11
3-A
Absolute Change vs. Relative Change
ex2/138 During a 6-month period, Nokias 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
yesterdays value.
The stocks value today is 20/10 2 200 of
the 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 (100P) 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 compared value and reference value
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 1770000-1120000650000
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.