Problem
Which is the correct work to convert 50 square inches into the equivalent number of square centimeters? $\frac{50 \mathrm{in}^{2}}{1} \cdot \frac{1 \mathrm{~cm}}{2.54 \mathrm{in}} \cdot \frac{1 \mathrm{~cm}}{2.54 \mathrm{in}}$ $\frac{50 \mathrm{in}^{2}}{1} \cdot \frac{2.54 \mathrm{~cm}}{\operatorname{lin}} \cdot \frac{2.54 \mathrm{~cm}}{\operatorname{lin}} \cdot \frac{2.54 \mathrm{~cm}}{\operatorname{lin}}$ $\frac{50 \mathrm{in}^{2}}{1} \cdot \frac{2.54 \mathrm{~cm}}{1 \mathrm{in}}$ $\frac{50 \mathrm{in}^{2}}{1} \cdot \frac{2.54 \mathrm{~cm}}{1 \mathrm{in}} \cdot \frac{2.54 \mathrm{~cm}}{1 \mathrm{in}}$
Solution
Step 1 ：The question is asking to convert square inches to square centimeters. The conversion factor from inches to centimeters is 2.54 cm = 1 in. However, since we are dealing with square units, we need to square the conversion factor. Therefore, the correct conversion should be \(\frac{50 \mathrm{in}^{2}}{1} \cdot \frac{2.54 \mathrm{~cm}}{1 \mathrm{in}} \cdot \frac{2.54 \mathrm{~cm}}{1 \mathrm{in}}\).
Step 2 ：Let's calculate this: \(conversion\_factor = 6.4516\), \(square\_inches = 50\), \(square\_centimeters = 322.58\)
Step 3 ：Final Answer: The equivalent number of square centimeters for 50 square inches is \(\boxed{322.58}\).
