To convert the pressure from pounds per square inch (psi) to newtons per square centimeter (N/cm²), follow these steps:
1. Identify the given values:
- Pressure: [tex]\( 28.0 \frac{\text{pounds}}{\text{inch}^2} \)[/tex]
- Conversion factor from pounds to newtons: [tex]\( 1 \text{pound} = 4.45 \text{newtons} \)[/tex]
- Conversion factor from square inches to square centimeters: [tex]\( 1 \text{inch}^2 = 6.45 \text{centimeters}^2 \)[/tex]
2. Convert the pressure from pounds per square inch to newtons:
- Multiply the given pressure by the conversion factor from pounds to newtons.
[tex]\( 28.0 \text{pounds/inch}^2 \times 4.45 \frac{\text{newtons}}{\text{pound}} \)[/tex]
- Intermediate result:
[tex]\[ 28.0 \times 4.45 = 124.6 \text{newtons/inch}^2 \][/tex]
3. Convert the area from square inches to square centimeters:
- Divide the result by the conversion factor from inches squared to centimeters squared.
[tex]\( \frac{124.6 \text{newtons/inch}^2}{6.45 \frac{\text{cm}^2}{\text{inch}^2}} \)[/tex]
4. Perform the division to obtain the pressure in newtons per square centimeter:
- Final result:
[tex]\[ \frac{124.6}{6.45} \approx 19.317829457364343 \frac{\text{newtons}}{\text{centimeter}^2} \][/tex]
5. Express the answer to the correct number of significant figures:
- The initial pressure value [tex]\( 28.0 \frac{\text{pounds}}{\text{inch}^2} \)[/tex] has 3 significant figures.
- Hence, the final result should be rounded to 3 significant figures.
Therefore, the pressure inside the tire in newtons per square centimeter is [tex]\( \boxed{19.3 \frac{\text { newtons }}{\text { centimeter }^2}} \)[/tex].
