Percent

• Percent is
  • a ratio of some number to 100.
  • Or it is parts per whole.
• It gives us a way to compare quantities when we might not know the entire population
  • If I say there are 7 freshmen in a class does that mean anything?
    • What if the class size is 700?
    • What if the class size is 7?
  • See, the number alone is meaningless.
• But if we say 70% of the class are freshmen...
  • That means that 70 out of 100
  • Or 7 out of 10 students are freshmen
  • This tells us that most of the students in the class, regardless of the size, are freshmen.
• In the real world
  • Taxes are expressed as a percentage
  • Interest rates are expressed as percentages
  • Sales, discounts, markups, ...
  • Tips, ...
• We will use percentages
  • In this chapter when we compute loans, ...
  • In chapter 11 when we do probabilities
  • In chapter 12 when we do statistics
  • They are fundamental to our work this semester.
• We need to be able to change between percent and decimal numbers.
• He gives three procedures
  • To change decimal numbers to a percent
    1. Multiply the decimal number by 100
    2. Add a % sign.
  • Change the decimal number to a percent

  • 0.345
    
    0.345  x 100=  34.5
    add a percent sign
    0.345 = 34.5%
    	 

  • To change a fraction to a percent
    1. Divide the fraction to get a decimal number
    2. Multiply the decimal number by 100
    3. Add a % sign.
  • Express 4/5 as a percent
  • 4/5 = 0.80 0.80 x 100 = 80 add a percent sign 4/5 = 80%

    	 
     To change a percent to a decimal number
    	 
    
    	      
     remove the % sign
    	      
     Divide by 100
    	 
    	 
     Express 86% as a decimal
    	 
     
    86%
    remove the percent sign
    86/100 = 0.86
    86^ = 0.86
    	 
    	 
     Be careful with 1/2%
        

• Frequently we hear of percent change
  • There was a 5% increase in the price of gas this week.
  • There was aa 10% decrease in rainfall this year.

  •                   new - old
    percent change = ---------- x 100%
                         old
    	

  • If the result is positive, it is a percent increase
  • If the result is negative, it is a percent decrease

  • In 1990 the US population was 249 million, in 2014 the population was 317 million.  Find the percent increase.
    	

• Remember

  
         part
        ------ x 100% = percent
         whole 
      

• Try problem 23 page 570
• Try problem 25 page 570
• Try problem 43, 45, 47 page 571