4-4 Percent Of Change

Warm-up Wednesday, October 28, 2009 Write an equation and solve each problem. 1.What is 20% of 20?

2.8 is what percent of 20? 3.18 is 90% of what number? 4.27 is 90% of what number?

4 – 4 Percent of Change Objectives: You will find the percent of change and find the percent error.

Percent Change • A percent of change tells us how much an amount has changed relative to the original amount.

• These are frequently used to describe changes: prices, stocks, populations, etc.

Percent of Change • Percent of Increase: When a value increases from its original amount.

• Percent of Decrease: When a value

decreases from its original amount (sometimes this is represented by a negative number).

Percent Change • Recall that to calculate a

percent change, we put the amount of change over the original amount. • In math terms that looks like:

amount of change % change = original amount

Example In 1965, when John entered college, the tuition per year was $7500. In 2000, when his daughter went to the same school, the tuition was $25,500. Find the percent change.

Example One of the largest stock market drops on Wall Street occurred on October 19, 1987. On this day, the stock market opened at 2246.74 points and closed at 1738.42 points. What was the percent change?

Greatest Possible Error • Because no measurement is exact,

you always measure to the nearest “something”.

• The greatest possible error in a

measurement is one-half of that measuring unit.

Examples ½ of 0.1 g or 0.05 g

½ of 1 cm or 0.5 cm

A. You use a beam

B. You measure a

balance to find the mass of a rock sample for a science lab. You read the scale as 3.8 g. What is the greatest possible error?

picture for the yearbook and record its height as 9 cm. What is your greatest possible error?

Finding Maximum & Minimum Areas 1. You must remember that area of a rectangle is equal to the length times width.

2. Add the GREATEST POSSIBLE ERROR to both

dimensions, then find the area (this is the Maximum Area)

3. Subtract the GREATEST POSSIBLE ERROR to both

dimensions, then find the area (this is the Minimum Area)

Example

13 ft

Maximum Area 13.5 • 7.5 = 101.25 ft2 Minimum Area 12.5 • 6.5 = 81.25 ft2

7 ft

Percent Error • It is another way to think of the error in measurement

• It is the ratio of the greatest possible error and the measurement

greatest possibleerror percenterror= actualmeasuremen t

Example A DVD has a diameter of 12.1 cm. Find the percent error in your measurement. GPE = ½ of 0.1 cm or 0.05 cm

0.05 12.1

≈ 0.004132231 = 0.4 % 4

1. Calculate the

greatest possible error 2. Use the percent error formula 3. Divide 4. Round to the nearest tenth and write as a percent. Don’t forget to move your decimal “to the right, to the right

Finding Percent Error in Calculating Volume. 1. Use Greatest Possible Error to convert dimensions into

maximum and minimum values 2. Find actual, maximum and minimum volumes by remembering VOLUME = length x width x height 3. Find the possible error by subtracting the actual volume from the maximum volume. 4. Divide the possible error by the actual volume 5. Round and write the error as a percent

Got It! Good! Page 207: 1-29 all Please note that your book represents decreases by using negative numbers. This is not required as long as the increase or decrease is specified.

Ticket to Leave 1. 5 is what percent of 67? 2. 79 is 44% of what number? 3. What is 0.2% of 834?