https://file.aiquickdraw.com/mathbot/file/1726384632644hqkx0zcu.jpg

Let's walk through the problem step by step to see how the difference occurred.

### Problem Overview:
You need to convert 6.0 square yards (a given area) to square meters using the provided conversion table:
- **Length conversion**: 1 meter = 1.09 yards.

Since the area is in square yards, we need to square the conversion factor for length.

### Step-by-Step Solution:
1. **Given**: The area of the wall is 6.0 square yards.
2. **Conversion Factor**: 1 meter = 1.09 yards, which implies:
   \[
   1 \, \text{yard} = \frac{1}{1.09} \, \text{meters}
   \]
3. **Convert to Square Meters**:
   - To convert square yards to square meters, you square the length conversion factor:
     \[
     \left(\frac{1 \, \text{meter}}{1.09 \, \text{yards}}\right)^2 = \left(\frac{1}{1.09}\right)^2 = 0.8417
     \]
   - Multiply the area by this factor:
     \[
     6.0 \, \text{square yards} \times 0.8417 = 5.05 \, \text{square meters}
     \]

4. **Rounding**:
   - Your final answer should match the correct number of significant figures. Since the input has 2 significant digits ("6.0"), the answer should also have 2 significant digits:
     \[
     5.1 \, \text{square meters}
     \]

### What Went Wrong:
Your response calculated the area to be **5.22 square meters**, which might indicate that either an incorrect conversion factor was used or rounding was done prematurely. The answer needs to be rounded to 2 significant figures, not 3, which explains why the correct answer is **5.1 square meters** instead of **5.22 square meters**.

### Conclusion:
Your response was incorrect because you gave too many significant figures in your final answer. The correct answer, rounded to 2 significant digits, is **5.1 square meters**.

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Do you want further details, or do you have any questions? Here are some related questions to consider:

1. How do you determine the number of significant digits required in a calculation?
2. Why is it important to square the length conversion factor when converting areas?
3. How would you convert cubic units (volume) between metric and customary systems?
4. What happens if you round the conversion factor instead of waiting until the final answer?
5. How can you use unit analysis to check your conversion calculations?

**Tip**: Always apply the appropriate rounding rules after completing all intermediate steps to avoid rounding errors in your final result.

Understand how to convert square yards to square meters and correctly round to significant figures. This problem involves using a conversion factor of 1 meter = 1.09 yards and squaring the result for area calculations, suitable for students in Grades 9-11.

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