Section 3A Uses and Abuses of Percentages Pages

per cent = “per 100” = “divided by 100” 47% = 47/100 =.47 2% = 2/100 = % = 813/100 = 8.13 percentage fractiondecimal 3-A

To convert a percentage to a decimal simply divide by 100 or move the decimal two places to the left To convert a simply multiply by 100% (=1) or move the decimal two places to the right: To convert a decimal to a percentage simply multiply by 100% (=1) or move the decimal two places to the right: 45% = 45/100 = % = 1.2/100 = =.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 simply divide to get a decimal and then move decimal two spaces to the right: 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 – “Percent of” 2. To describe change over time 3. For comparison 3-A

1. Percent “of “ - (multiply) A newspaper reports that 44% of 1069 people surveyed said that the president was doing a good job. How many people said this? 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 = = 44% * 1069 =.44*1069 = = 470 people 3-A

More Practice 37/148 A is 75 and B is 480. A is ____________ percent of B. B is ____________ percent of A. 46/ blooming tulips in a field of 398 tulips. field. The blooming tulips are _______ percent of the field. 3-A

2. Percents are often used to describe how a quantity changes over time 3-A absolute change= new value – original value Given: original value and new value relative change

Absolute Change vs. Relative Change 3-A John’s salary grew from $20000 in 2000 to $28000 in /148 John’s salary grew from $20000 in 2000 to $28000 in absolute change = $28000 – $20000 = $8000 relative change = $8000/$20000 =.40 = 40% John’s salary in 2003 was 40% more than his salary in 2000 [John’s salary in 2003 was 28000/20000 = 1.40 = 140% of his salary in 2000.]

Absolute Change vs. Relative Change ex4/137 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 ex2/136 Today, my 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

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. Percentage Of vs. More (or Less) Than (page 140) 3-A

3. Percents are often used to compare two values. Given: compared value and reference value absolute difference = compared value  ‘reference’ value 3-A

57/149 The daily circulation of the Wall Street Journal is ≈ 1.77 million. The daily circulation of the New York Times is ≈ 1.07 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 = = Relative difference = / =.654 = 65.4% The WSJ has more readers than the NYT. The WSJ has 65.4% more readers than the NYT. 3-A

Solving Percentage Problems 77/150 You purchase a bicycle with a labeled (pre-tax) price of $699. The local sales tax rate is 7.6%. What is your final cost? 78/150 The final cost of your new shoes is $ The local sales tax rate is 6.2%. What was the labeled (pre-tax) price. 81/150 Your dinner bill is $ You leave $22. What percent tip did you leave? 3-A

Homework Pages # 50, 55, 56, 58, 61, 79, 80, 82 Express your answers in sentence form. 3-A