Section 3Af2008pI by xiagong0815

VIEWS: 1 PAGES: 15

									          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

 Express your answers in sentence form.

								
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