Introduction:

Calculating the percent error is a popular method to determine the accuracy of an experiment, in which the difference between an observed value and the true value is expressed as a percentage. This measurement is crucial in scientific experiments, as it can provide insight into the reliability of results and indicate potential improvements in methodology. In this article, we will discuss the general formula to calculate percent error and provide some examples to help you understand this concept better.

Formula:

The percent error formula is straightforward to understand, and it consists of dividing the absolute difference between the measured (observed) value and the true (accepted) value by the true value. Afterwards, multiply the result by 100% to obtain the percentage.

Percent Error = (| Measured Value – True Value | / True Value) × 100%

Here is a step-by-step guide on how to calculate percent error:

1. Identify the measured (observed) value and the true (accepted) value.

2. Subtract the measured value from the true value.

3. Obtain the absolute difference by discarding any negative signs.

4. Divide this absolute difference by the true value.

5. Multiply by 100% to convert it into a percentage.

Example:

Imagine you are conducting an experiment to measure gravity’s acceleration on Earth. The known accepted value of Earth’s gravitational acceleration is 9.81 m/s². After performing various measurements, you obtain an average result of 9.67 m/s² as your measured value.

Now let’s calculate percent error using this data.

Measured Value = 9.67 m/s²

True Value = 9.81 m/s²

Step 1: Subtract Measured Value from True Value:

9.81 – 9.67 = 0.14

Step 2: Obtain Absolute Difference:

|0.14| = 0.14

Step 3: Divide Absolute Difference by True Value:

0.14 / 9.81 ≈ 0.0143

Step 4: Multiply by 100% to Convert to Percentage:

0.0143 × 100% ≈ 1.43%

Result: The percent error in this experiment is approximately 1.43%.

Conclusion:

Percent error is a useful tool in evaluating the accuracy of an experiment or measurement. By comparing results against true values, we can assess the precision of our methods and identify areas for improvement. Always remember to follow the steps outlined above and convert your final result into a percentage when calculating percent error to ensure clear communication of your findings.