To convert the pressure from pounds per square inch to newtons per square centimeter, follow these detailed steps:
1. Identify the given values:
- Pressure: [tex]\(28.0 \frac{\text{pounds}}{\text{inch}^2}\)[/tex]
- Conversion factor: [tex]\(1 \text{ pound} = 4.45 \text{ newtons}\)[/tex]
- Conversion factor: [tex]\(1 \text{ inch}^2 = 6.45 \text{ centimeters}^2\)[/tex]
2. Convert pounds per square inch to newtons per square centimeter.
[tex]\[
\text{Pressure in } \frac{\text{newtons}}{\text{cm}^2} = 28.0 \frac{\text{pounds}}{\text{inch}^2} \times \frac{4.45 \text{ newtons}}{1 \text{ pound}} \times \frac{1 \text{ inch}^2}{6.45 \text{ cm}^2}
\][/tex]
3. Perform the multiplication and division:
[tex]\[
28.0 \times \frac{4.45}{6.45} = 28.0 \times 0.6899224806 \approx 19.318
\][/tex]
4. Round the result to the correct number of significant figures:
- The given pressure 28.0 has 3 significant figures.
- Therefore, we round 19.318 to 19.3 to maintain 3 significant figures.
The pressure is 19.3 [tex]\(\frac{\text{newtons}}{\text{centimeter}^2}\)[/tex].
