What is the percent error of the data?
| Trial # | Density |
|---|---|
| 1 | 10.34 |
| 2 | 10.58 |
| 3 | 10.62 |
| Average | 10.51 |
Answer (2)
Calculate the absolute error: ∣10.51 − 10.49∣ = 0.02 .
Divide the absolute error by the accepted value: 10.49 0.02 = 0.001906577693040951 .
Multiply by 100 to express as a percentage: 0.001906577693040951 × 100 = 0.1906577693040951 .
Round the result to four decimal places: The percent error is 0.1907% .
Explanation
Understanding the Problem We are given the accepted density of silver as 10.49 c m 3 g and the average experimental density as 10.51 c m 3 g . We want to calculate the percent error of the data.
Formula for Percent Error The formula for percent error is given by: Percent Error = Accepted Value ∣ Experimental Value − Accepted Value ∣ × 100 In our case, the experimental value is the average density, which is 10.51 c m 3 g , and the accepted value is 10.49 c m 3 g .
Calculating Percent Error Now, we plug in the values into the formula: Percent Error = 10.49 ∣10.51 − 10.49∣ × 100 Percent Error = 10.49 0.02 × 100 Percent Error = 0.001906577693040951 × 100 Percent Error = 0.1906577693040951 Rounding to four decimal places, we get 0.1907% .
Final Answer Therefore, the percent error of the data is approximately 0.1907% .
Examples
Percent error calculations are essential in various scientific and engineering fields. For instance, when conducting experiments in a chemistry lab, calculating the percent error helps determine the accuracy of measurements. If a student measures the density of a substance and compares it to the known, accepted density, the percent error indicates how close the experimental result is to the true value. This helps in refining experimental techniques and ensuring the reliability of results. Similarly, in manufacturing, percent error is used to assess the precision of instruments and processes, ensuring products meet quality standards.
The percent error of the density data is approximately 0.1905%. This is calculated by finding the absolute error between the experimental and accepted values, dividing by the accepted value, and converting to a percentage. This helps assess how accurate the experimental results are compared to the known standard.
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