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3. Perform the following calculations and report your answers to the correct number of significan figures and with the correct units: a) 105.116 g - 45.67 g = d = 3.456 g - 2.5 mL b)

3. Perform the following calculations and report your answers to the correct number of significan figures and with the correct units: a) 105.116 g - 45.67 g = d = 3.456 g - 2.5 mL b)

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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### Significant Figures in Scientific Calculations **3. Perform the following calculations and report your answers to the correct number of significant figures and with the correct units:** a) \( 105.116 \, \text{g} - 45.67 \, \text{g} = \) __________ b) \( d = \frac{3.456 \, \text{g}}{2.5 \, \text{mL}} = \) __________ --- **4. What is the only way to reduce random error in measurements?** --- In this exercise, students are asked to perform calculations that involve significant figures and accurate reporting of measurement units. Below we detail the processes and principles needed to solve these problems: 1. **Subtraction of Masses (Part 3a)**: - To find the difference between two masses, subtract the given values ensuring that the result is reported with the correct number of significant figures. - Example Calculation Steps: - Subtract \( 45.67 \, \text{g} \) from \( 105.116 \, \text{g} \). - Determine the number of significant figures in each measurement and report your final answer accordingly. 2. **Density Calculation (Part 3b)**: - To calculate the density (\(d\)), use the formula \( d = \frac{m}{V} \), where \( m \) is the mass and \( V \) is the volume. - Example Calculation Steps: - Divide \( 3.456 \, \text{g} \) by \( 2.5 \, \text{mL} \). - Ensure the final result is reported with the correct number of significant figures based on the least precise measurement in your calculation. **Part 4**: - **Reducing Random Error**: - Random errors can be reduced by taking multiple measurements and averaging them. This improves reliability and accuracy in scientific experiments. The only way to lessen random error is by increasing the sample size or the number of trials, thereby minimizing the impact of outliers or anomalies. By understanding and applying the concept of significant figures, students will be able to report their experimental results more accurately.
Transcribed Image Text:### Significant Figures in Scientific Calculations **3. Perform the following calculations and report your answers to the correct number of significant figures and with the correct units:** a) \( 105.116 \, \text{g} - 45.67 \, \text{g} = \) __________ b) \( d = \frac{3.456 \, \text{g}}{2.5 \, \text{mL}} = \) __________ --- **4. What is the only way to reduce random error in measurements?** --- In this exercise, students are asked to perform calculations that involve significant figures and accurate reporting of measurement units. Below we detail the processes and principles needed to solve these problems: 1. **Subtraction of Masses (Part 3a)**: - To find the difference between two masses, subtract the given values ensuring that the result is reported with the correct number of significant figures. - Example Calculation Steps: - Subtract \( 45.67 \, \text{g} \) from \( 105.116 \, \text{g} \). - Determine the number of significant figures in each measurement and report your final answer accordingly. 2. **Density Calculation (Part 3b)**: - To calculate the density (\(d\)), use the formula \( d = \frac{m}{V} \), where \( m \) is the mass and \( V \) is the volume. - Example Calculation Steps: - Divide \( 3.456 \, \text{g} \) by \( 2.5 \, \text{mL} \). - Ensure the final result is reported with the correct number of significant figures based on the least precise measurement in your calculation. **Part 4**: - **Reducing Random Error**: - Random errors can be reduced by taking multiple measurements and averaging them. This improves reliability and accuracy in scientific experiments. The only way to lessen random error is by increasing the sample size or the number of trials, thereby minimizing the impact of outliers or anomalies. By understanding and applying the concept of significant figures, students will be able to report their experimental results more accurately.
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