Last updated on August 5th, 2025
In mathematics and science, the percent error formula is used to measure the accuracy of an experimental value in comparison to a theoretical value. It expresses the error as a percentage of the theoretical value. In this topic, we will learn the formula for calculating percent error.
The percent error formula is used to determine the accuracy of an experimental measurement. Let’s learn the formula to calculate the percent error.
Percent error is calculated to understand the deviation of an experimental value from a theoretical value. It is calculated using the formula:
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100
In science and real-life applications, the percent error formula is crucial for evaluating the accuracy and precision of measurements. Here are some important aspects of using percent error:
- It helps in comparing the accuracy of different measurements.
- By understanding percent error, students and professionals can improve experimental methods and data analysis.
- It provides insight into the reliability and validity of experimental data.
Students might find the percent error formula tricky to memorize, but with some tips and tricks, it can be easier.
- Use the mnemonic: "Experimental minus Theoretical, divide by Theoretical and times 100."
- Practice with real-life examples to see how the formula is applied.
- Create flashcards with the formula for quick memorization and recall.
In real life, the percent error formula plays a significant role in various fields. Here are some applications of the percent error formula:
- In laboratories, to evaluate the accuracy of chemical measurements.
- In engineering, to assess the precision of design specifications and manufacturing processes.
- In finance, to gauge the accuracy of financial models or forecasts.
Students often make errors when calculating percent error. Here are some mistakes and ways to avoid them to master the percent error formula.
An experiment measured the boiling point of water as 102°C. The theoretical boiling point is 100°C. What is the percent error?
The percent error is 2%
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(102 - 100) / 100| × 100 = |2 / 100| × 100 = 2%
A scale shows a weight of 48 kg for a standard 50 kg weight. What is the percent error of the scale?
The percent error is 4%
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(48 - 50) / 50| × 100 = |-2 / 50| × 100 = 4%
A chemist finds the concentration of a solution to be 0.95 M, but the actual concentration is 1.00 M. Calculate the percent error.
The percent error is 5%
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(0.95 - 1.00) / 1.00| × 100 = |-0.05 / 1.00| × 100 = 5%
A thermometer reads 20°C when the actual temperature is 22°C. What is the percent error of the thermometer?
The percent error is 9.09%
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(20 - 22) / 22| × 100 = |-2 / 22| × 100 ≈ 9.09%
A measurement of 9.8 m/s² is recorded for gravitational acceleration, while the accepted value is 9.81 m/s². Find the percent error.
The percent error is 0.10%
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(9.8 - 9.81) / 9.81| × 100 = |-0.01 / 9.81| × 100 ≈ 0.10%
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