1. Section 3A Uses and Abuses of Percentages Pages 133-147

2. per cent = “per 100” = “divided by 100” 47% = 47/100 =.47 2% = 2/100 =.02 813% = 813/100 = 8.13 percentage fractiondecimal/ proportion 3-A

3. 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), To convert a decimal to a percentage simply multiply by 100% (=1), or move the decimal two places to the right: or move the decimal two places to the right: 45% = 45/100 =.45 1.2% = 1.2/100 =.012 714% = 714/100 = 7.14.16 =.16 * 100% = 16% 2.3 = 2.3 * 100% = 230% 3-A

4. To convert a percentage to a fraction simply divide by 100 (and reduce as necessary): 45% = 45/100 = 9/20 1.3% = 1.3/100 = 13/1000 525% = 525/100 = 21/4 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

5. 3 Ways of Using Percentages 1. As fractions – “Percent of” 2. To describe change over time 3. For comparison 3-A

6. 1. Percent “of “ - (multiply) In 2004, 9.7% of the citizens in Virginia lived in poverty. The population of Virginia was 7,495,827. How many people in Virginia were living in poverty? ‘9.7% × 7,459,827’ =.097 × 7,459,827 = 727,095.219 =.097 × 7,459,827 = 727,095.219 = = 727,095 people 3-A

7. More Practice Suppose A is 75 and B is 480. A is ____________ percent of B. B is ____________ percent of A. 3-A So, A is 15.625% of B. and B is 640% of A.

8. More Practice 3 45 blooming tulips in a field of 398 tulips. field. The blooming tulips are __??___ percent of the field. 3-A

9. 2. Percents are often used to describe how a quantity changes over time 3-A Given: original value and new value

10. Absolute Change vs. Relative Change 3-A John’s salary grew from $20,000 in 2001 to $28,000 in 2003. absolute change = $28,000 – $20,000 = $8000 relative change = $8000/$20,000 =.40 = 40% John’s salary in 2003 was 40% more than his salary in 2001. [ John’s salary in 2003 was 28,000/20,000 = 1.40 = 140% of his salary in 2001.]

11. Absolute Change vs. Relative Change 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

12. 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

13. Absolute Change vs. Relative Change Today, my stock doubled in price from $1000 to $2000. absolute change = $2000 – $1000 = $1000 relative change = $1000/$1000 = 1 = 100% The value of stock today is 100% more than yesterday’s value. (Today’s price is 200% of yesterday’s price.) 3-A

14. Absolute Change vs. Relative Change How much would stock have to grow to in order to see a relative change of 200%? absolute change = $2000 =$3000– $1000 relative change = 200% = 2 = $2000/$1000 So my stock had to triple in value. 3-A

15. Homework Pages 148-150 # 22, 30, 50, 52, 56 Express your answers in sentence form. 3-A