Percent

• You need to understand and be able to work with percent.
  • It is a basic tool for comparing quantities throughout life
  • And it is a critical tool for several of the chapters we will cover.
• A percent is a ratio of some number to 100.
  • 15% is really 15/100
• A percent is also parts of the whole.
  • Book Example: Ross got 18 out of 20 questions right on a test.
    • part: 18, whole: 20, 18/20 = 90%
  • If you remember part/whole X 100 = percent most percent problems are easy to solve.
  • You should memorize this formula
  • You should also add this to your "cheat sheet"
    • Page 607 number 28: In a study of U.S. rivers, 693,905 miles of river were studied. According to the U.S. Environmental Protection Agency, it was found that 36% of the total miles of rivers studied had impaired water quality. How many miles of rivers had impaired quality?

      part: unknown (x)
      whole: 693,905
      percent: 36%
      
           x
        ------- * 100 = 36%    just solve for x.
        693,905 
      	     

    • 
    • What percent of students preferred country music?

      part = 176
      whole = 1960
      percent = x
      
            176
           ---- * 100 = x%
           1960
                  

    • Problem 51: Five percent of what number is 15?

      part = 15
      while = x
      percent 5%
      
            15
           --- * 100 = 5%
            x
      	    

• They give three procedures:
  • To change a decimal number to a percent
    • Multiply by 100
    • Add the percent sign
    • change 0.15 to a percent: 0.15x100 = 15 or 15%
    • Watch for things like changing 0.001 to a percent (0.1%)
  • To change a percent to a decimal number
    • Remove the percent sign
    • Divide by 100
    • Change 34% to a decimal: 34/100 or 0.034
    • Watch for things like changing 0.1% to a decimal : (0.001)
    • Watch for things like 1/4% = 0.25% which is 0.0025.
  • To change a fraction to a percent
    • Change the fraction to a decimal number:
      • Divide the numerator by the denominator.
    • Change the decimal number to a percent.
    • Change 34/92 to a percent: 34/92 = 0.36956 or 36.96%
• Percent Change
  • Percent change is a common measure of a single value that is changing.
  • For example the price of gas today compared to the price of gas last week.
  • The number of unemployed today verses the number a year ago.
  • There is always a new value and a old value.
  • If the new value is larger than the old value it is a percent increase, and the result will be positive.
  • If the new value is smaller than the old value it is a percent decrease, and the result will be negative.
  • Formula: percent change = (new value - old value)/ old value x 100
  • You should memorize this formula
  • You should also add this to your "cheat sheet"
  • Example:
    • Page 608 number 41: Russian Population The population of Russia has been decreasing since the fall of the Soviet Union. In 1990, the Russian population was about 148 million people. In 2010, the population of Russia was about 143 million people. Determine the percent decrease in Russia's population during the time period:

    • new: 143 million
      old: 148 million
      
             percent change = (new - old)/old x 100%
                            = (143-148)/148 x 100% = -5/148 x 100% = -3.38%
      
             Since the question asked for percent decrease, the answer is 3.38%
      	    

Problems

• Convert 1/8 to a percent
• Convert 13/80 to a percent, round to the nearest hundredth.
• Convert 0.5279 to a percent.
• Convert 4.54 to a percent.
• Convert 32% to a decimal.
• Convert 4/3% to a decimal (CAREFUL)
• Convert 345.9% to a decimal
• The recommended daily allowance (RDA) of niacin for adults is 20MG. One serving of a breakfast cereal provides 14mg of niacin, What percent of the RDA of niacin does one serving provide?
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