To convert the pressure inside a tire from [tex]\(\frac{\text {pounds}}{\text {inch}^2}\)[/tex] to [tex]\(\frac{\text {newtons}}{\text {centimeter}^2}\)[/tex], follow these steps:
1. Identify the given values:
- Pressure: 28.0 [tex]\(\frac{\text {pounds}}{\text {inch}^2}\)[/tex]
- Conversion factor for pounds to newtons: [tex]\(1 \text{ pound} = 4.45 \text{ newtons}\)[/tex]
- Conversion factor for square inches to square centimeters: [tex]\(1 \text{ inch}^2 = 6.45 \text{ cm}^2\)[/tex]
2. Convert pounds to newtons:
Multiply the given pressure by the conversion factor from pounds to newtons to get the pressure in [tex]\(\frac{\text{newtons}}{\text{inch}^2}\)[/tex]:
[tex]\[
28.0 \, \frac{\text{pounds}}{\text{inch}^2} \times 4.45 \, \frac{\text{newtons}}{\text{pound}} = 124.6 \, \frac{\text{newtons}}{\text{inch}^2}
\][/tex]
3. Convert square inches to square centimeters:
Since we want to express the pressure in [tex]\(\frac{\text{newtons}}{\text{centimeter}^2}\)[/tex], we need to account for the area conversion:
[tex]\[
\frac{124.6 \, \frac{\text{newtons}}{\text{inch}^2}}{6.45 \, \frac{\text{cm}^2}{\text{inch}^2}} \approx 19.32 \, \frac{\text{newtons}}{\text{centimeter}^2}
\][/tex]
4. Express the answer to the correct number of significant figures:
The given pressure (28.0 [tex]\(\frac{\text {pounds}}{\text {inch}^2}\)[/tex]) has three significant figures. Thus, the final answer should also have three significant figures.
Therefore, the pressure in [tex]\(\frac{\text {newtons}}{\text {centimeter}^2}\)[/tex] is [tex]\( \boxed{19.32} \)[/tex].
