Calculate 8.2221 g/(13.7 L + 0.27 L) with the correct number of significant figures and units

To calculate the expression \( \frac{8.2221 \, \text{g}}{13.7 \, \text{L} + 0.27 \, \text{L}} \) with the correct number of significant figures:

1. **Add the volumes**:  
   \( 13.7 \, \text{L} + 0.27 \, \text{L} = 13.97 \, \text{L} \)  
   Here, the result should be rounded to the least number of decimal places in the original measurements, which is 13.7 L with 1 decimal place.  
   Therefore, the sum is rounded to \( 14.0 \, \text{L} \).

2. **Divide the mass by the volume**:  
   \( \frac{8.2221 \, \text{g}}{14.0 \, \text{L}} = 0.586 \, \text{g/L} \)

3. **Significant figures**:  
   - The mass (8.2221 g) has 5 significant figures.
   - The volume (14.0 L) has 3 significant figures.
   - The final answer should be rounded to 3 significant figures, as dictated by the volume, the limiting factor in the division.

Thus, the final answer is:

\[ 0.587 \, \text{g/L} \]

Would you like more details or have any questions?

### Follow-up Questions:
1. What are the rules for determining the number of significant figures in addition and subtraction?
2. How do you determine the number of significant figures in multiplication and division?
3. Why is it important to maintain significant figures in calculations?
4. How would the result change if the volume was given with different significant figures?
5. Can you explain how to calculate the error propagation in this type of calculation?

**Tip:** Always consider the least number of significant figures when performing operations, as the final answer should not be more precise than the least precise measurement.

Learn how to calculate 8.2221 grams divided by the sum of 13.7 liters and 0.27 liters, ensuring correct significant figures. This problem covers significant figures in division, essential for accurate scientific calculations. Suitable for Grades 9-12.

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