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Let's go through the questions step by step. The goal is to multiply or divide the values and ensure the answers are reported with the correct number of significant figures.

### Problem 1:
\[
2.0947 \, \text{cm} \times 3.925 \, \text{cm}
\]
- The number of significant figures in \(2.0947\) is **5**.
- The number of significant figures in \(3.925\) is **4**.
- When multiplying, the result should have the same number of significant figures as the value with the fewest significant figures, which is **4**.

Let's calculate:
\[
2.0947 \times 3.925 = 8.21619775 \, \text{cm}^2
\]
Rounding to **4 significant figures**:
\[
8.216 \, \text{cm}^2
\]

### Problem 2:
\[
477.8 \, \text{g} \div 88.93 \, \text{mL}
\]
- The number of significant figures in \(477.8\) is **4**.
- The number of significant figures in \(88.93\) is **4**.
- The result should have **4 significant figures**.

Let's calculate:
\[
477.8 \div 88.93 = 5.372957017 \, \text{g/mL}
\]
Rounding to **4 significant figures**:
\[
5.373 \, \text{g/mL}
\]

### Problem 3:
\[
20.947 \, \frac{\text{mol}}{\text{L}} \times 47. \, \text{L}
\]
- The number of significant figures in \(20.947\) is **5**.
- The number of significant figures in \(47.\) is **2**.
- The result should have **2 significant figures**.

Let's calculate:
\[
20.947 \times 47 = 985.509 \, \text{mol}
\]
Rounding to **2 significant figures**:
\[
990 \, \text{mol}
\]

### Final Answers:
1. \( 8.216 \, \text{cm}^2 \)
2. \( 5.373 \, \text{g/mL} \)
3. \( 990 \, \text{mol} \)

Would you like more details on significant figures or the steps involved in the calculations?

Here are 5 related questions to deepen your understanding:
1. Why is the number of significant figures important in scientific calculations?
2. How does multiplying and dividing affect the number of significant figures?
3. What is the difference between precision and accuracy in measurements?
4. How do you round numbers when dealing with significant figures?
5. Can you explain how significant figures differ when adding and subtracting compared to multiplying and dividing?

Tip: Always count significant figures carefully, especially when different units are involved!

Multiply or divide the following measurements. Be sure each answer you enter contains the correct number of significant digits. 1) 2.0947 cm × 3.925 cm 2) 477.8 g ÷ 88.93 mL 3) 20.947 mol/L × 47. L

Learn how to multiply and divide measurements while considering significant figures. This problem includes three calculations: 2.0947 cm × 3.925 cm, 477.8 g ÷ 88.93 mL, and 20.947 mol/L × 47. L. Suitable for high school students.

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