101 LearnersLast updated on August 5th, 2025
Math Formula for Percent Error
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.
List of Math Formulas for 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.
Math Formula for 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
Importance of Percent Error Formula
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.
Tips and Tricks to Memorize Percent Error Formula
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.
Real-Life Applications of Percent Error Formula
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.
Common Mistakes and How to Avoid Them While Using Percent Error Formula
Students often make errors when calculating percent error. Here are some mistakes and ways to avoid them to master the percent error formula.
Mistake 1
Not using absolute values
Students sometimes forget to use absolute values, resulting in negative percent errors, which are incorrect. To avoid this mistake, always use absolute values in the formula: |(Experimental Value - Theoretical Value)|.
Mistake 2
Confusing percent error with percentage difference
Students might confuse percent error with percentage difference. Remember, percent error measures the accuracy of an experimental value against a theoretical one, not the difference between two experimental values.
Mistake 3
Forgetting to multiply by 100
A common error is forgetting to multiply by 100 to convert the decimal into a percentage. Always remember to include this step to express the error as a percentage.
Mistake 4
Incorrectly identifying theoretical and experimental values
Ensure that you correctly identify which value is the theoretical value and which is the experimental value. Mixing these up can lead to incorrect calculations.
Mistake 5
Rounding errors in calculation
When calculating percent error, rounding too early can lead to inaccuracies. Keep as many decimal places as possible until the final step to ensure accuracy.
Examples of Problems Using Percent Error Formula
Problem 1
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%
Explanation
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(102 - 100) / 100| × 100 = |2 / 100| × 100 = 2%
Problem 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%
Explanation
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(48 - 50) / 50| × 100 = |-2 / 50| × 100 = 4%
Problem 3
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%
Explanation
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(0.95 - 1.00) / 1.00| × 100 = |-0.05 / 1.00| × 100 = 5%
Problem 4
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%
Explanation
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(20 - 22) / 22| × 100 = |-2 / 22| × 100 ≈ 9.09%
Problem 5
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%
Explanation
Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100 = |(9.8 - 9.81) / 9.81| × 100 = |-0.01 / 9.81| × 100 ≈ 0.10%
FAQs on Percent Error Formula
1.What is the percent error formula?
2.Why is absolute value used in the percent error formula?
3.How to reduce percent error in experiments?
4.Can percent error be negative?
5.What does a high percent error indicate?
Glossary for Percent Error Formula
- Percent Error: A measure of how inaccurate a measurement is, expressed as a percentage of the theoretical value.
- Experimental Value: The value measured during an experiment.
- Theoretical Value: The accepted or true value based on reliable references.
- Absolute Value: A mathematical function that returns the non-negative value of a number, disregarding its sign.
- Deviation: The difference between the experimental value and the theoretical value.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
