Percent of Change and Error

Bellwork Monday The Indy 500 is one of the world’s greatest motor races. The table shows the average speed of the winning race cars for various years. 1. Write the ratio 2. Write the ratio speed increase from 1922 to 1955 speed increase from 1955 to 2010 speed in 1922 speed in 1955 Then write the ratio as a percent. Then write the ratio as a percent. 3. Why are the amounts of the increase the same but the percents different?

Lesson 5 Percent of Change Words: The percent of change is a ratio that compares the change in a quantity to the original amount. Equation: percent of change = When you compare the amount of change to the original amount in a ratio, you are finding the percent of change. The percent of change is based on the original amount. If the original quantity is increased, then it is called the percent of increase. If the original quantity is decreased, then it is called a percent of decrease. Percent of increase = Percent of decrease = amount of change original amount amount of increase original amount amount of decrease original amount

Example 1 Find the percent of change in the cost of gasoline from 1970 ($1.30) to 2010 ($2.95). Round to the nearest whole percent if necessary. Step 1: Find the amount of increase. $2.95 - $1.30 = $1.65 Step 2: Find the percent of increase. percent of increase = amount of increase original amount = 1.65 1.30 ≈1.27 ≈127%

Example 2 Sandy bought a DVD recorder for $280. Now, it is on sale for $220. Find the percent of change in the price. Round to the nearest whole percent if necessary.

On your own 1. Find the percent of change from 10 yards to 13 yards. 2. The prince of a radio was $20. It is on sale for $15. What is the percent of change in the price of the radio?

Percent Error Words: The percent error is a ratio that compares the inaccuracy of an estimate, or amount of error, to the actual amount. Equation: percent of error = amount of error actual amount

Example 3 Whitney wants to practice free-throws. He estimates the distance from the free-throw line to the hoop and marks it with chalk. Whitney’s estimate was 13.5 feet. The actual distance should be 15 feet. Find the percent of error. Step 1: Find the amount of error. 15 feet – 13.5 feet = Step 2: Find the percent error 1.5 feet percent error = amount of error actual amount = 1.5 15 =0.1 or 10%

Example 4 Suppose you guess there are 300 gum balls in a jar, but there are actually 400. What is the percent of error?

On your own Find the percent of error if the estimate is $230 and the actual amount is $245. Round to the nearest whole percent.