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You measure the density of an unknown rock to be 2.3g/mL. The accepted/true value of the rock is supposed to be 2.54 g/mL. What is your percent error? 22% .09% 9.45% -9.45%

You measure the density of an unknown rock to be 2.3g/mL. The accepted/true value of the rock is supposed to be 2.54 g/mL. What is your percent error? 22% .09% 9.45% -9.45%

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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**Calculating Percent Error in Density Measurement** When conducting experiments, it's critical to quantify how accurate your measurements are. This can be done by calculating the percent error, which gives you a clear understanding of how your measured value compares to the accepted or true value. **Problem Example:** You measure the density of an unknown rock to be 2.3 g/mL. The accepted or true density value for the rock is 2.54 g/mL. What is your percent error? **Multiple Choice Options:** - 22% - 0.09% - 9.45% - -9.45% **Solution:** To calculate the percent error, use the following formula: \[ \text{Percent Error} = \left( \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right) \times 100\% \] - Measured Value = 2.3 g/mL - True Value = 2.54 g/mL Plugging the values into the formula: \[ \text{Percent Error} = \left( \frac{2.3 - 2.54}{2.54} \right) \times 100\% \] \[ \text{Percent Error} = \left( \frac{-0.24}{2.54} \right) \times 100\% \] \[ \text{Percent Error} = -9.45\% \] The correct answer is -9.45%. **Conclusion:** A negative percent error indicates that the measured density is lower than the true density. This is essential for identifying potential systematic errors in the measurement process.
Transcribed Image Text:**Calculating Percent Error in Density Measurement** When conducting experiments, it's critical to quantify how accurate your measurements are. This can be done by calculating the percent error, which gives you a clear understanding of how your measured value compares to the accepted or true value. **Problem Example:** You measure the density of an unknown rock to be 2.3 g/mL. The accepted or true density value for the rock is 2.54 g/mL. What is your percent error? **Multiple Choice Options:** - 22% - 0.09% - 9.45% - -9.45% **Solution:** To calculate the percent error, use the following formula: \[ \text{Percent Error} = \left( \frac{\text{Measured Value} - \text{True Value}}{\text{True Value}} \right) \times 100\% \] - Measured Value = 2.3 g/mL - True Value = 2.54 g/mL Plugging the values into the formula: \[ \text{Percent Error} = \left( \frac{2.3 - 2.54}{2.54} \right) \times 100\% \] \[ \text{Percent Error} = \left( \frac{-0.24}{2.54} \right) \times 100\% \] \[ \text{Percent Error} = -9.45\% \] The correct answer is -9.45%. **Conclusion:** A negative percent error indicates that the measured density is lower than the true density. This is essential for identifying potential systematic errors in the measurement process.
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