Lesson 14

Percent Error

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

14.1: Number Talk: Estimating a Percentage of a Number

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 3,000 people. The exact attendance is 2,486 people. What is the percent error?


A micrometer is an instrument that can measure lengths to the nearest micron (a micron is a millionth of a meter). Would this instrument be useful for measuring any of the following things? 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).

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 Entries

  • measurement error

    Measurement error is the positive difference between a measured amount and the actual amount.

    For example, Diego measures a line segment and gets 5.3 cm. The actual length of the segment is really 5.32 cm. The measurement error is 0.02 cm, because \(5.32-5.3=0.02\).

  • percent error

    Percent error is a way to describe error, expressed as a percentage of the actual amount.

    For example, a box is supposed to have 150 folders in it. Clare counts only 147 folders in the box. This is an error of 3 folders. The percent error is 2%, because 3 is 2% of 150.