2.10 Change Expressed as a Percent I can find percent change and find the relative error in linear and nonlinear measurements.
Percent Change • Expresses an amount of change as a percent of an original amount. • If a new amount is greater, the change is a percent increase. • If a new amount is less, it is a percent decrease. • Ratio of the amount of change to the original amount
Finding a Percent Change • A coat is on sale for $74.50. The original price was $82. what is the discount expressed as a percent change? • This is a percent decrease. • ≈0.09, or 9% decrease
You Try! • A store buys an electric guitar for $295 and marks up the price to $340. What is the markup expressed as a percent change? • ≈15%
Relative Error • Ratio of the absolute value of the difference of a measured (or estimated) value and an actual value compared to the actual value. • When expressed as a percent, it is called percent error.
Practice • A decorator estimates that a rectangular rug is 5 ft by 8 ft, but it is actually 4 ft by 8 ft. Find the percent error. • 25%
Minimum and Maximum Dimensions • Often, actual measurements are not known. • You cannot always be completely accurate. • Think about measuring with a ruler. Precision is limited and sometimes you have to round. • The most any measurement can be off is by half of the unit used to measure.
Example • You measure the length of a poster to be 18.5 in to the nearest half inch. What are the minimum and maximum possible lengths of the poster? • You measured to the nearest half inch, so the greatest possible error is 0.25 in (half of your units) in either direction.
Greatest Possible Percent Error • The dimensions of a gift box are shown to the nearest inch. What is the greatest possible percent error in calculating the box’s volume? • What do we know? • Greatest possible error is 0.5 in • V = lwh • What are we looking for? • Solve
Continued • Find differences for minimum and maximum volumes. • Use greater difference for greatest possible percent error
Assignment • ODDS ONLY • P.148 #7-23