# Percentage Error

Warmup

(1.) Decide if y is an increase or a decrease of x. Then determine the percentage.

(2.) Decide if y is an increase or a decrease of x. Then determine the percentage.

Activity #1

Application in Solving Problems.

A micrometer is an instrument that can measure lengths to the nearest micron (a micron is a millionth of a meter).

Would a micrometer be useful for measuring the following? If so, what would the largest percent error be?

(1.) The thickness of an eyelash, which is typically about 0.1 millimeters.

(2.) The diameter of a red blood cell, which is typically about 8 microns.

(3.) The diameter of a hydrogen atom, which is about 100 picometers (a picometer is a trillionth of a meter).

Activity #2

Application in Solving Problems.

A metal measuring tape expands when the temperature goes above 50°F. For every degree Fahrenheit above 50, its length increases by 0.00064%.

(1.) The temperature is 100 degrees Fahrenheit. How much longer is a 30-foot measuring tape than its correct length?

(2.) What is the percent error?

Activity #3

More Exercises.

• Read and solve the following set of problems.

Challenge #1

A police officer’s radar gun measured the speed of a car at 63 miles per hour. If the car was actually going 62.8 miles per hour, what was the percent error in this measurement?

Challenge #2

It took 48 minutes to drive downtown. A navigation app estimated it would be less than that. If the error was 20%, what was the app’s estimate?

Challenge #3

A farmer estimated that there were 25 gallons of water left in a tank. If this is an underestimate by 16%, how much water was actually in the tank?