What is a Percent

1
What is a Percent?
2
Objectives

• When finished with this presentation, you should
  be able to
• Convert a percent to a fraction
• Convert a percent to a decimal
• Convert a decimal to a percent
• Compute what percent one number is of another
  number
• Compute percent of a number
• Compute percent increase

3
What is a Percent?

• A percent is comparing a number to the number one
  hundred we call this a ratio.
• The word PER means divided by - like when I say
  I was only going 65 miles PER hour - that means
  I travel 65 miles for each hour I drive.

4
What is a Percent?

• The word CENT means one hundred. It is the same
  root word we use for century (100 years), or a
  cent (one one-hundredth of a dollar).
• So together PERCENT means, literally, divided by
  100.
• The symbol is used for PERCENT.

5
Convert a Percent to a Fraction

• For example, 25 is the ratio of 25 to 100. This
  usually is written as 25/100. If you reduce this
  fraction it becomes 1/4. (25 divides into 100, 4
  times)
• Therefore 25 and 1/4 are essentially the same
  thing.
• If you ask your friend for 25 of her pizza its
  the same as asking for one-fourth of her pizza.

6
Convert a Percent to a Fraction

• So a general rule is, if you want to convert a
  percent into a fraction just DIVIDE the number by
  100.
• Example 5 is 5/100, which can reduced to
  1/20. (5 divides into 100, 20 times)

7
Convert a Percent to a Fraction

• Here is another example using a percent that is
  not a whole number.
• Example 12.5 is 12.5/100. To reduce this
  fraction, you would make the top and bottom of
  this fraction whole numbers. Multiply the top
  and bottom by 10, and we get 125/1000. Now 125
  divides into 1000, 8 times, so the fraction of
  125/1000 reduces to 1/8.

8
Convert a Percent to a Fraction

• Lets look at our example of 25 again.
• We said this could also be written as 25/100 or ¼.

9
Convert a Percent to a Fraction

• If you divide 25 by 100, or 1 by 4 you get a
  decimal value of 0.25 (try it on your
  calculator).
• So, that means that 25 is the same as ¼ and 0.25

10
Convert a Percent to a Decimal

• Did you notice that 25 is the same as 0.25?
• Heres another example
• We already said that 5 is 5/100 or 1/20. If you
  divide 5 by 100, or 1 by 20 you get 0.05

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Convert a Percent to a Decimal

• Therefore, 5 is the same as 0.05
• Do you see a pattern here?
• Heres a general rule
• to convert a percent to a decimal value just
  move the decimal point 2 places to the LEFT
• Remember the decimal point is here in a whole
  number

2 1
12
Convert a Decimal to a Percent

• What if you wanted to convert a decimal to a
  percent?
• For instance, how would you convert 0.35 to a
  percent?
• All you need to do is reverse the process we just
  learned.

13
Convert a Decimal to a Percent

• Review
• To convert a percent to a decimal you moved the
  decimal point two places to the LEFT.
• So, as a general rule, to convert a decimal value
  to a percent, move the decimal two places to the
  RIGHT.
• Therefore, 0.35 35

14
Compute What Percent One Number is of Another
Number

• What if you wanted to find out what percent a
  certain number was of another number?
• Lets say for instance that you made 420 this
  week and paid 157.50 in taxes. You would like
  to know how much, as a percent, you paid in
  taxes. In other words, what percent is 157.50 of
  420?

15
Compute What Percent One Number is of Another
Number

• You simply DIVIDE 157.50 by 420. 157.50/420
  0.375
• Now move the decimal point two places to the
  RIGHT to make it a percent (remember percent
  means per one-hundred).
• So we have 37.5. You paid 37.5 of your
  earnings in taxes.

16
Compute What Percent One Number is of Another
Number

• Look at this another way, keeping in mind that
  percent means per one-hundred.
• If you paid 37.5 in taxes this means that for
  every 100 you earn, you will pay 37.50 in taxes.

17
Compute Percent of a Number

• What if you wanted to know how much is X of some
  number?
• For instance, lets say your credit card gives
  you 1.5 cash back for your monthly bill, and you
  would like to know how much you will receive this
  month.
• This months bill is 870.

18
Compute Percent of a Number

• So, the problem is to figure out
• What is 1.5 of 870?
• All you need to do is MULTIPLY 1.5 by 870.

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Compute Percent of a Number

• 1.5 0.015
• (move the decimal point two places LEFT)
• So,
• 0.015 x 870 13.05
• You will get 13.05 cash back this month.

20
Compute Percent Increase

• Lets look at an example where the percent is
  greater than 100.
• Example 125 is 125/100, which can be reduced
  to 5/4 or written as decimal is 1.25 (remember to
  move the decimal two places to the LEFT).

21
Compute Percent Increase

• Heres an example of this kind of problem
• Lets say you have a product that you currently
  sell for 12. (This is called the OLD PRICE)
• You would like to increase the OLD PRICE by 30.
• What NEW PRICE should you sell your product for
  so that it is 30 more than the OLD PRICE?

22
Compute Percent Increase

• The OLD PRICE was 12. You need to calculate a
  NEW PRICE that is 30 more than 12.
• Note
• The OLD PRICE equals 100.
• The increase is 30.
• So, the NEW PRICE is 130 of the OLD PRICE.
• This is the same as saying What is 130 of 12?
• So, you need to calculate 130 of 12.

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Compute Percent Increase

• 130 1.3 in decimal form. (Remember, move the
  decimal point two places to the LEFT.)
• So, 1.3 x 12 15.6
• You should sell your product at the NEW PRICE of
  15.60.

24
Websites for Further Perusal

• MathLeague What is a percent?
• The MathPage Example problems involving percent
• Good practice problems here
• http//www.themathpage.com/ARITH/Ar_Pr/mpow_2.htm

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Summary

• Convert a Percent to a Fraction Divide the
  number by 100.
• Convert a Percent to a Decimal Move the decimal
  point two places to the LEFT.
• Convert a Decimal to a Percent Move the decimal
  point two places to the RIGHT.

26
Summary

• Compute what Percent one number is of another
  number
• Divide the first number by the second number
• Compute a Percentage of a number
• Multiply the number by the percent in decimal
  form.
• Compute Percent increases
• Multiply the original value by the percent
  increase.