Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. \[ \begin{aligned} 0.934 \frac{\mathrm{~g}}{\mathrm{~mL}} \times 4.75 \mathrm{~mL} & =4.43 \mathrm{~g} \\ 142.41 \mathrm{~g} \div 0.38 \mathrm{~mL} & =370 \frac{\mathrm{~g}}{\mathrm{~mL}}\end{aligned} \]

Let's verify each calculation by considering both the mathematical operations and the rules for significant figures. ### 1. Multiplication: \( 0.934 \, \frac{\text{g}}{\text{mL}} \times 4.75 \, \text{mL} \) **Step-by-Step Calculation:** 1. **Multiply the Numerical Values:** \[ 0.934 \times 4.75 = 4.4435 \, \text{g} \] 2. **Determine Significant Figures:** - **0.934** has **3 significant figures**. - **4.75** has **3 significant figures**. - In multiplication, the result should have the **same number of significant figures as the factor with the least number of significant figures**. 3. **Apply Significant Figures:** \[ 4.4435 \, \text{g} \rightarrow 4.43 \, \text{g} \quad (\text{rounded to 3 significant figures}) \] **Final Answer:** \[ 0.934 \, \frac{\text{g}}{\text{mL}} \times 4.75 \, \text{mL} = \mathbf{4.43 \, \text{g}} \] ### 2. Division: \( \frac{142.41 \, \text{g}}{0.38 \, \text{mL}} \) **Step-by-Step Calculation:** 1. **Divide the Numerical Values:** \[ \frac{142.41}{0.38} = 374.2368421 \, \frac{\text{g}}{\text{mL}} \] 2. **Determine Significant Figures:** - **142.41** has **5 significant figures**. - **0.38** has **2 significant figures**. - In division, the result should have the **same number of significant figures as the divisor or dividend with the least number of significant figures**. 3. **Apply Significant Figures:** \[ 374.2368421 \, \frac{\text{g}}{\text{mL}} \rightarrow 370 \, \frac{\text{g}}{\text{mL}} \quad (\text{rounded to 2 significant figures}) \] *Note:* The trailing zero in "370" indicates that there are two significant figures. **Final Answer:** \[ \frac{142.41 \, \text{g}}{0.38 \, \text{mL}} = \mathbf{370 \, \frac{\text{g}}{\text{mL}}} \] ### **Summary** Both of your calculations correctly apply the rules for significant figures: 1. \( 0.934 \, \frac{\text{g}}{\text{mL}} \times 4.75 \, \text{mL} = 4.43 \, \text{g} \) (3 significant figures) 2. \( \frac{142.41 \, \text{g}}{0.38 \, \text{mL}} = 370 \, \frac{\text{g}}{\text{mL}} \) (2 significant figures) Great job!