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Let's work through the conversion of \( 10 \, \text{cm}^2 \) to square inches (\( \text{in}^2 \)).

The table provides the following conversion:
\[ 1 \, \text{in}^2 = 6.5 \, \text{cm}^2 \]

Now, to convert \( 10 \, \text{cm}^2 \) to square inches, you use the following dimensional analysis:

\[
10 \, \text{cm}^2 \times \frac{1 \, \text{in}^2}{6.5 \, \text{cm}^2} = \frac{10}{6.5} \, \text{in}^2
\]

Let's calculate:

\[
\frac{10}{6.5} \approx 1.54 \, \text{in}^2
\]

Thus, \( 10 \, \text{cm}^2 \) is approximately \( 1.54 \, \text{in}^2 \), rounded to the nearest hundredth.

Would you like further clarification or more details on this process?

### Here are 5 follow-up questions:
1. How would you convert 20 cm² to square inches using the same method?
2. What is the process to convert square inches to square centimeters?
3. How would you use dimensional analysis to convert larger areas, like square meters to square inches?
4. What would be the conversion factor for cubic measurements (e.g., cm³ to in³)?
5. Can you describe why dimensional analysis is a reliable method for unit conversion?

### Tip:
When doing dimensional analysis, always ensure that the units you want to cancel are arranged properly to avoid confusion.

Convert 10 cm² to in² using dimensional analysis based on the given conversion table.

Learn how to convert 10 cm² to in² using dimensional analysis. This problem utilizes the conversion formula: 1 in² = 6.5 cm², with step-by-step calculations. Suitable for college-level students studying measurement and unit conversions.

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