Percent Error
In short: Percent error shows how far a measured or estimated value is from the true value, found by dividing the absolute difference by the true value and writing it as a percent.
7th GradeRatios and Percents7.RP.A.3
What is Percent Error?
The percent error of a guess, a reading or a prediction puts a number on how close it came to the exact value, relative to that exact value, because no measurement is perfect.
The formula is \(\frac{|\text{measured} – \text{true}|}{\text{true}} \times 100\%\). The absolute value bars remove the sign, so overshooting and undershooting by the same amount give the same answer. A small percent means an accurate result.
How to spot it
- A problem mentions an estimate, a prediction or a lab reading alongside an accepted or exact value.
- You are asked how accurate a guess was, expressed in percent instead of in units.
- A science class compares a measured length, mass or time with a value from a reference table.
- Two people measure the same object and the question asks whose result is closer in relative terms.
The method
- Identify the true (accepted) value and the measured (estimated) value.
- Subtract them and take the absolute value of the difference.
- Divide that difference by the true value, not by the measured one.
- Multiply by \(100\) and write the percent sign.
Percent Error: solved example
Problem
Ravi measures the width of his classroom as 247 centimeters for a door frame whose labeled width is 250 centimeters. What is his percent error?
Solution
Absolute difference: \(|247 – 250| = 3\) centimeters.
Divide by the true value: \(\frac{3}{250} = 0.012\). The percent error is 1.2%.
Try it
Question 1
A student predicts a bridge is 420 feet long. Its real length is 400 feet. Find the percent error.
Show the answer
\(\frac{|420 – 400|}{400} = \frac{20}{400} = 0.05\), so the error is 5%.
Question 2
A thermometer reads \(98.0^{\circ}\) F in a water bath whose true temperature is \(100.0^{\circ}\) F. What is the percent error?
Show the answer
\(\frac{2}{100} = 0.02\), so the error is 2%.
Percent Error vs. Percent Change
Percent change links two values of the same quantity at different times, and the original value is the denominator. Percent error links an observed value with the true value at one moment, and the true value is the denominator. Percent error also drops the sign; percent change keeps it to show growth or shrinkage.
Keep going
Lessons
Worksheets and quizzes
- Percent Problems: Tax, Tips, Discounts and Markups – Worksheet
- Percent Problems: Tax, Tips, Discounts and Markups – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Ratios and Percents