Lesson 14: Percent Error

Let’s use percentages to describe other situations that involve error.

Estimate.

25% of 15.8

9% of 38

1.2% of 127

0.53% of 6

0.06% of 202

14.2: Plants, Bicycles, and Crowds

1. Instructions to care for a plant say to water it with $\frac34$ cup of water every day. The plant has been getting 25% too much water. How much water has the plant been getting?
2. The pressure on a bicycle tire is 63 psi. This is 5% higher than what the manual says is the correct pressure. What is the correct pressure?
3. The crowd at a sporting event is estimated to be 2,500 people. The exact attendance is 2,486 people. What is the percent error?

14.3: Measuring in the Heat

A metal measuring tape expands when the temperature goes above $50^\circ\text{F}$. 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?

Summary

Percent error can be used to describe any situation where there is a correct value and an incorrect value, and we want to describe the relative difference between them. For example, if a milk carton is supposed to contain 16 fluid ounces and it only contains 15 fluid ounces:

• the measurement error is 1 oz, and
• the percent error is 6.25% because $1 \div 16 = 0.0625$.

We can also use percent error when talking about estimates. For example, a teacher estimates there are about 600 students at their school. If there are actually 625 students, then the percent error for this estimate was 4%, because $625 - 600 = 25$ and $25 \div 625 = 0.04$.

Glossary

percent error

percent error

The difference between the correct value and the incorrect value, expressed as a percentage of the correct value.