Learn on PengiReveal Math, AcceleratedUnit 3: Solve Problems Involving Percentages

Lesson 3-6: Solve Percent Error Problems

In Lesson 3-6 of Reveal Math Accelerated, 7th grade students learn how to calculate percent error by finding the difference between an estimated or claimed value and an actual value, then applying the percent equation to express that difference as a percentage. Students work through real-world examples such as seed counts on sunflowers and acceptable word counts in an essay to understand how percent error measures the inaccuracy of a value relative to a reference value. The lesson also explores how percent error applies in practical contexts like federal speedometer compliance standards.

Section 1

Identify the Reference Value for Percent Error

Property

The reference value (the denominator) in a percent error calculation is always the accurate, exact, or target amount, not the estimated or measured amount.

Percent Error=Amount of ErrorReference Value\text{Percent Error} = \frac{\text{Amount of Error}}{\text{Reference Value}}

Section 2

Find Percent Error

Property

Percent error measures how much an estimated value differs from the actual value:

Percent Error=Amount of ErrorActual Amount×100%\text{Percent Error} = \frac{\text{Amount of Error}}{\text{Actual Amount}} \times 100\%

where Amount of Error = ∣Estimated Value−Actual Value∣|\text{Estimated Value} - \text{Actual Value}|

Section 3

Interpret Percent Error and Tolerances

Property

A measurement is within an acceptable tolerance (allowable range) if its deviation from the target value is less than or equal to half of the tolerance:

Deviation≤Tolerance2\text{Deviation} \leq \frac{\text{Tolerance}}{2}

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Identify the Reference Value for Percent Error

Property

The reference value (the denominator) in a percent error calculation is always the accurate, exact, or target amount, not the estimated or measured amount.

Percent Error=Amount of ErrorReference Value\text{Percent Error} = \frac{\text{Amount of Error}}{\text{Reference Value}}

Section 2

Find Percent Error

Property

Percent error measures how much an estimated value differs from the actual value:

Percent Error=Amount of ErrorActual Amount×100%\text{Percent Error} = \frac{\text{Amount of Error}}{\text{Actual Amount}} \times 100\%

where Amount of Error = ∣Estimated Value−Actual Value∣|\text{Estimated Value} - \text{Actual Value}|

Section 3

Interpret Percent Error and Tolerances

Property

A measurement is within an acceptable tolerance (allowable range) if its deviation from the target value is less than or equal to half of the tolerance:

Deviation≤Tolerance2\text{Deviation} \leq \frac{\text{Tolerance}}{2}

Examples