1. Change Expressed as a Percent Section 2-10

2. Goals Goal To find percent change. To find the relative error in linear and nonlinear measures. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary Percent change Percent increase Percent decrease Relative error Percent error

4. Definition Percent Change - an increase or decrease given as a percent of the original amount. Percent Increase - describes an amount that has grown. Percent Decrease - describes an amount that has be reduced.

5. Percent Change amount of increase = new amount – original amount amount of decrease = original amount – new amount

6. Find each percent change. Tell whether it is a percent increase or decrease. From 8 to 10 = 0.25 = 25% Write the answer as a percent Simplify the numerator. Simplify the fraction. 8 to 10 is an increase, so a change from 8 to 10 is a 25% increase. Example: Find Percent Change

7. Helpful Hint Before solving, decide what is a reasonable answer. For Example, 8 to 16 would be a 100% increase. So 8 to 10 should be much less than 100%.

8. From 75 to 30 = 0.6 = 60% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 75 to 30 is a decrease, so a change from 75 to 30 is a 60% decrease. Find the percent change. Tell whether it is a percent increase or decrease. Example: Find Percent Change

9. From 200 to 110 = 0.6 = 60% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 200 to 110 is an decrease, so a change from 200 to 110 is a 60% decrease. Find each percent change. Tell whether it is a percent increase or decrease. Your Turn:

10. From 25 to 30 = 0.20 = 20% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 25 to 30 is an increase, so a change from 25 to 30 is a 20% increase. Find each percent change. Tell whether it is a percent increase or decrease. Your Turn:

11. From 80 to 115 = 0.4375 = 43.75% Write the answer as a percent. Simplify the numerator. Simplify the fraction. 80 to 115 is an increase, so a change from 80 to 115 is a 43.75% increase. Find each percent change. Tell whether it is a percent increase or decrease. Your Turn:

12. A. Find the result when 12 is increased by 50%. 0.50(12) = 6 Find 50% of 12. This is the amount of increase. 12 + 6 =18 It is a percent increase, so add 6 to the original amount. 12 increased by 50% is 18. B. Find the result when 55 is decreased by 60%. 0.60(55) = 33 Find 60% of 55. This is the amount of decrease. 55 – 33 = 22 It is a percent decrease so subtract 33 from the the original amount. 55 decreased by 60% is 22. Example: Find Percent Change

13. A. Find the result when 72 is increased by 25%. 0.25(72) = 18 Find 25% of 72. This is the amount of increase. 72 + 18 =90 It is a percent increase, so add 18 to the original amount. 72 increased by 25% is 90. B. Find the result when 10 is decreased by 40%. 0.40(10) = 4 Find 40% of 10. This is the amount of decrease. 10 – 4 = 6 It is a percent decrease so subtract 4 from the the original amount. 10 decreased by 40% is 6. Your Turn:

14. Common application of percent change are percent discount and percent markup. A discount is an amount by which an original price is reduced. discount = % of original price final price = original price – discount A markup is an amount by which a wholesale price is increased. final price = wholesale cost markup + wholesale cost = % of Percent Change Application

15. The entrance fee at an amusement park is $35. People over the age of 65 receive a 20% discount. What is the amount of the discount? How much do people over 65 pay? Method 1 A discount is a percent decrease. So find $35 decreased by 20%. 0.20(35) = 7 Find 20% of 35. This is the amount of the discount. 35 – 7 = 28 Subtract 7 from 35. This is the entrance fee for people over the age of 65. Example: Discount

16. Method 2 Subtract the percent discount from 100%. 100% – 20% = 80% People over the age of 65 pay 80% of the regular price, $35. 0.80(35) = 28 Find 80% of 35. This is the entrance fee for people over the age of 65. 35 – 28 = 7 Subtract 28 from 35. This is the amount of the discount. By either method, the discount is $7. People over the age of 65 pay $28.00. Example: Discount

17. A student paid $31.20 for art supplies that normally cost $52.00. Find the percent discount. $52.00 – $31.20 = $20.80 Think: 20.80 is what percent of 52.00? Let x represent the percent. 20.80 = x(52.00) 0.40 = x 40% = x The discount is 40% Since x is multiplied by 52.00, divide both sides by 52.00 to undo the multiplication. Write the answer as a percent. Example: Discount

18. A $220 bicycle was on sale for 60% off. Find the sale price. Method 2 Subtract the percent discount from 100%. 100% – 60% = 40% The bicycle was 60% off of 100%. 0.40(220) = 88 Find 40% of 220. By this method, the sale price is $88. Your Turn:

19. Ray paid $12 for a $15 T-shirt. What was the percent discount ? $15 – $12 = $3 Think: 3 is what percent of 15? Let x represent the percent. 3 = x(15) 0.20 = x 20% = x The discount is 20%. Since x is multiplied by 15, divide both sides by 15 to undo the multiplication. Write the answer as a percent. Your Turn:

20. The wholesale cost of a DVD is $7. The markup is 85%. What is the amount of the markup? What is the selling price? Method 1 A markup is a percent increase. So find $7 increased by 85%. 0.85(7) = 5.95 7 + 5.95 = 12.95 Find 85% of 7. This is the amount of the markup. Add to 7. This is the selling price. Subtract from 12.95. This is the amount of the markup. 12.95  7 = 5.95 By either method, the amount of the markup is $5.95. The selling price is $12.95. Method 2 Add percent markup to 100% The selling price is 185% of the wholesale price, 7. 100% + 85% = 185% Find 185% of 7. This is the selling price. 1.85(7) = 12.95 Example: Markup

21. A video game has a 70% markup. The wholesale cost is $9. What is the selling price? Method 1 A markup is a percent increase. So find $9 increased by 70%. 0.70(9) = 6.30 Find 70% of 9. This is the amount of the markup. 9 + 6.30 = 15.30 Add to 9. This is the selling price. The amount of the markup is $6.30. The selling price is $15.30. Your Turn:

22. What is the percent markup on a car selling for $21,850 that had a wholesale cost of $9500? 21,850 – 9,500 = 12,350 Find the amount of the markup. 12,350 = x(9,500) 1.30 = x 130% = x The markup was 130 percent. Think: 12,350 is what percent of 9,500? Let x represent the percent. Since x is multiplied by 9,500 divide both sides by 9,500 to undo the multiplication. Write the answer as a percent. Your Turn:

23. Errors in Measurement Any measurement made with a measuring device is approximate. If you measure the same object two different times, the two measurements may not be exactly the same. The difference between two measurements is called a variation in the measurements. Another word for this variation, or uncertainty in measurement, is "error." This "error" is not the same as a "mistake." It does not mean that you got the wrong answer. The error in measurement is a mathematical way to show the uncertainty in the measurement. It is the difference between the result of the measurement and the true value of what you were measuring.

24. Expressing the Error in Measurements One method of expressing the error in a measurement is relative error. The relative error of a measurement shows how large the error is in relation to the correct value. The percent error is the relative error expressed as a percentage (relative error ⨯ 100 and written as a %).

25. Relative Error

26. Example A decorator estimates that a rectangular rug is 5 ft by 8 ft. The rug is actually 4 ft by 8 ft. What is the percent error in the estimated area? The relative error is.25. The percent error is the relative error expressed as a percentage. The percent error is 25%. The estimated area is off by 25%.

27. Your Turn: You think that the distance between your home and a friend’s house is 5.5 mi. The actual distance is 4.75 mi. What is the percent error in your estimation?

28. Your Turn: A cube’s volume is estimated to be 8 cm3. When measured, each side was 2.1 cm in length. What is the percent error in the estimated volume?

29. Joke Time Why don't aliens eat clowns. Because they taste funny. What did the beach say when the tide came in? Long time no sea! Why was the belt arrested? For holding up the pants.

30. Assignment 2.10 Exercises Pg. 160 – 162: #6 – 36 even