Percentage Of

1
Percentage Of

• Review for converting between fractions and
  percentages
• To convert a percentage to a fraction, replace
  the symbol with division by 100. Simply the
  fraction when necessary. 25 25/100 1/4
• To convert a percentage to a decimal, drop the
  symbol and move the decimal place to the left two
  places (that is, divide by 100). 25 0.25
• To convert a decimal to a percentage, move the
  decimal point two places to the right and add the
  symbol. 0.43 43

2
Percentage Of
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whole
whole
part
3
Percentage Of

• DePauls undergraduate student body is
  approximately 21,000 students. 54 of the
  student body is female. How many females attend
  DePaul?
• 21,000 0.54
• 11,340

4
Percentage Of

• In 1993, 248.7 million people in the US were born
  in the US, and the rest, 19.8 million, were
  foreign born. What percentage of the total
  population of the US was foreign born?
• x 248.7 million 19.8 million
• .0737 7.37

5
Percentage Of

• The sales tax in Illinois is 8.75. The cashier
  rings up your purchase and tells you that your
  total bill is 103. What was the amount of your
  bill before taxes were added?

6
Percentage Of

• The sales tax in Illinois is 8.75. The cashier
  rings up your purchase and tells you that your
  total bill is 103. What was the amount of your
  bill before taxes were added?
• Total bill before-tax purchase price (1 r)
• 103 purchase price (1.0875)
• purchase price 103/1.0875
• 94.71

7
Percentage Of

• You are in another state. You are buying a
  computer at Best Buy. The price before taxes is
  949. When the cashier rings up your purchase
  you owe 1005.94. What is the sales tax in this
  state?
• 949 (1 r) 1005.94
• (1r) 1.06
• x 6

8
Percentage Change

• Suppose the population of a town was 10,000 in
  1970 and 15,000 in 2000. We can express the
  change in population in three ways
• Absolute change new value reference value
• Relative change
• Percentage change

new value reference value reference value
new value reference value reference value
X 100
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Example

• World Population in 1950 was 2.6 billion. By the
  beginning of 200, it had reached 6.0 billion.
  What is the absolute and percentage change in
  world population from 1950 to 2000?

10
Example

• World Population in 1950 was 2.6 billion. By the
  beginning of 200, it had reached 6.0 billion.
  What is the absolute and percentage change in
  world population from 1950 to 2000?
• Absolute change 6.0 2.6 3.4 billion

11
Example

• World Population in 1950 was 2.6 billion. By the
  beginning of 200, it had reached 6.0 billion.
  What is the absolute and relative change in world
  population from 1950 to 2000?
• Percentage change (6.0 2.6)/2.6 x 100
• Percentage change 130.7

12
Percentage Change

• If a quantity doubles, what is the relative
  change and percentage change?

13
Using Percentages for Comparisons

• Life expectancy for American men is about 75
  years, while life expectancy for Russian men is
  about 59 years. Compare the life expectancy of
  American men to that of Russian men in absolute
  and relative terms.

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Using Percentages for Comparisons

• Life expectancy for American men is about 75
  years, while life expectancy for Russian men is
  about 59 years. Compare the life expectancy of
  American men to that of Russian men in absolute
  and relative terms.
• Absolute difference 75 59 16 years

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Using Percentages for Comparisons

• Life expectancy for American men is about 75
  years, while life expectancy for Russian men is
  about 59 years. Compare the life expectancy of
  American men to that of Russian men in absolute
  and relative terms.
• Percentage difference (75 -59)/59 x 100 27

16
Of versus More Than

• Consider a population that triples in size from
  200 to 600. There are two equivalent ways to
  state this change with percentages
• Using more than The new population is 200 more
  than the original population.
• Percentage change (600 200)/200 x 100 200

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Of versus More Than

• Consider a population that triples in size from
  200 to 600. There are two equivalent ways to
  state this change with percentages
• Using of The new population is 300 of the
  original population.
• Percentage new population / original population
• Percentage 600 / 200 300

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Of versus More Than

• Notice that the percentages in the more than
  and of statements are related by 300 100
  200. This leads to the following general
  relationship
• If the new or compared value is P more than the
  reference value, then it is (100 P) of the
  reference value.
• If the new or compared value is P less than the
  reference value, then it is (100 P) of the
  reference value.

19
Quick Thought Question

• One store advertises 1/3 off everything!
• Another store advertises Sale prices just 1/3 of
  original prices!
• Which store is having the bigger sale?

20
Example

• In 2001, there were 654 drive-in theaters in the
  US, 77 fewer than in 1985. Approximately how
  many drive-in theaters were there in 1985?
• in 2001 in 1985 (1 - 0.77)
• 654 in 1985 (1 - 0.77)
• 654/0.33 in 1985 1982 theaters

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Reverse Percentage Change Example

• According to the official 2000 census, the
  Hispanic population of the US in 2000 was
  35,305,818. It rose by an astounding 57.9 from
  1990 to 2000. What was the Hispanic population
  in 1990?

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Another Percentage Change Example

• According to the official 2000 census, the
  Hispanic population of the US in 2000 was
  35,305,818. It rose by an astounding 57.9 from
  1990 to 2000. What was the Hispanic population
  in 1990?
• (1 0.579) x 35,305,818
• x 35,305,818 / 1.579
• x 22,359,606

23
Percentages of Percentages

• Suppose your bank increases the interest rate on
  your savings account from 3 to 4. Its
  tempting to say that your interest rate increases
  by 1, but this is ambiguous. Why?

24
Percentages of Percentages

• Suppose your bank increases the interest rate on
  your savings account from 3 to 4. Its
  tempting to say that your interest rate increases
  by 1, but this is ambiguous. Why?
• The interest rate increases by 1 percentage
  point. This is an absolute difference.

25
Percentages of Percentages

• Suppose your bank increases the interest rate on
  your savings account from 3 to 4. Its
  tempting to say that your interest rate increases
  by 1, but this is ambiguous. Why?
• The percentage change in the interest rate is
  _____? This is a relative difference.

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If you cant convince them, confuse
them. -Harry S Truman

• Based on interviews with a sample of students at
  DePaul, you conclude that the percentage of all
  students who are vegetarians is between 20 and
  30. Should you report the result as 25 with a
  margin of error of 5 or as 25 with a margin of
  error of 5 percentage points?