Question
Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. \[ \begin{aligned} 0.934 \frac{\mathrm{~g}}{\mathrm{~mL}} \times 4.75 \mathrm{~mL} & =4.43 \mathrm{~g} \\ 142.41 \mathrm{~g} \div 0.38 \mathrm{~mL} & =370 \frac{\mathrm{~g}}{\mathrm{~mL}}\end{aligned} \]
Ask by Cook Ryan. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The calculations are correct.
- \( 0.934 \, \frac{\text{g}}{\text{mL}} \times 4.75 \, \text{mL} = 4.43 \, \text{g} \)
- \( \frac{142.41 \, \text{g}}{0.38 \, \text{mL}} = 370 \, \frac{\text{g}}{\text{mL}} \)
Both answers have the right number of significant digits.
Solution
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!
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Explain 
Simplify this solution Mind Expander
To multiply the measurements 0.934 g/mL by 4.75 mL, you start with the multiplication: \( 0.934 \, \text{g/mL} \times 4.75 \, \text{mL} = 4.43 \, \text{g} \). Since the measurement 4.75 has three significant figures, your final answer should reflect this number of significant figures. Thus, rounding appropriately gives you 4.43 g. Next, for the division of 142.41 g by 0.38 mL, you perform the calculation: \( 142.41 \, \text{g} \div 0.38 \, \text{mL} \approx 374.79 \, \text{g/mL} \). However, since 0.38 has two significant figures, the final answer should also be limited to two significant figures, resulting in 370 g/mL.
