Understanding Percent Error
Percent error is a measure of the difference between a measured or calculated value and the actual value. It is often used in science, engineering, and other fields to express the accuracy of a measurement or calculation. In this worksheet, we will explore how to calculate percent error and provide solutions to common problems.
Calculating Percent Error
The formula for calculating percent error is:
Percent Error = (|Measured Value - Actual Value| / Actual Value) x 100
Where:
- Measured Value is the value obtained from a measurement or calculation
- Actual Value is the true or accepted value
- | | denotes the absolute value, which ensures the result is always positive
Example Problems
Problem 1
A student measures the length of a room to be 12.5 meters, but the actual length is 12.2 meters. Calculate the percent error.
Solution
Percent Error = (|12.5 - 12.2| / 12.2) x 100 = (0.3 / 12.2) x 100 = 2.46%
Problem 2
A scientist calculates the density of a substance to be 2.5 g/cm³, but the actual density is 2.3 g/cm³. Calculate the percent error.
Solution
Percent Error = (|2.5 - 2.3| / 2.3) x 100 = (0.2 / 2.3) x 100 = 8.70%
Problem 3
A engineer measures the voltage of a circuit to be 12.8 volts, but the actual voltage is 12.5 volts. Calculate the percent error.
Solution
Percent Error = (|12.8 - 12.5| / 12.5) x 100 = (0.3 / 12.5) x 100 = 2.40%
Tables and Charts
The following table summarizes the calculations for the example problems:
| Problem | Measured Value | Actual Value | Percent Error |
|---|---|---|---|
| 1 | 12.5 m | 12.2 m | 2.46% |
| 2 | 2.5 g/cm³ | 2.3 g/cm³ | 8.70% |
| 3 | 12.8 V | 12.5 V | 2.40% |
Notes
📝 Note: When calculating percent error, it is essential to use the absolute value of the difference between the measured and actual values to ensure the result is always positive.
📝 Note: Percent error can be used to express the accuracy of a measurement or calculation. A lower percent error indicates a more accurate result.
In conclusion, percent error is a valuable tool for evaluating the accuracy of measurements and calculations. By using the formula and following the examples provided, you can calculate percent error with confidence. Remember to use the absolute value of the difference between the measured and actual values and to express the result as a percentage.
What is percent error?
+Percent error is a measure of the difference between a measured or calculated value and the actual value, expressed as a percentage.
How do I calculate percent error?
+Use the formula: Percent Error = (|Measured Value - Actual Value| / Actual Value) x 100
Why is it essential to use the absolute value when calculating percent error?
+Using the absolute value ensures the result is always positive, which is essential for expressing the accuracy of a measurement or calculation.
Related Terms:
- Percent error Worksheet PDF
- Percent error Worksheet 7th grade
- Percent error calculator
