To convert the pressure from pounds per square inch ([tex]$\frac{\text{pounds}}{\text{inch}^2}$[/tex]) to newtons per square centimeter ([tex]$\frac{\text{newtons}}{\text{cm}^2}$[/tex]), follow these steps:
1. Identify the given pressure:
The pressure inside the tire is [tex]$28.0 \frac{\text{pounds}}{\text{inch}^2}$[/tex].
2. Determine the conversion factors:
- 1 pound = 4.45 newtons
- 1 inch[tex]$^2$[/tex] = 6.45 cm[tex]$^2$[/tex]
3. Convert the pressure from pounds to newtons:
Since 1 pound is equivalent to 4.45 newtons, we can multiply the given pressure by this conversion factor:
[tex]\[
28.0 \frac{\text{pounds}}{\text{inch}^2} \times 4.45 \frac{\text{newtons}}{\text{pound}}
\][/tex]
4. Convert the area from square inches to square centimeters:
Since 1 inch[tex]$^2$[/tex] is equivalent to 6.45 cm[tex]$^2$[/tex], we need to divide by this area conversion factor to convert from per inch[tex]$^2$[/tex] to per cm[tex]$^2$[/tex]:
[tex]\[
\frac{\text{newtons}}{\text{inch}^2} \div 6.45 \frac{\text{cm}^2}{\text{inch}^2}
\][/tex]
5. Combine the conversions:
Combine both conversions into a single step:
[tex]\[
28.0 \frac{\text{pounds}}{\text{inch}^2} \times \frac{4.45 \frac{\text{newtons}}{\text{pound}}}{6.45 \frac{\text{cm}^2}{\text{inch}^2}}
\][/tex]
6. Calculate the result:
After performing the multiplication and division, we find:
[tex]\[
\frac{28.0 \times 4.45}{6.45} = 19.31782945736434
\][/tex]
7. Express the answer with the correct number of significant figures:
The given pressure (28.0 [tex]$\frac{\text{pounds}}{\text{inch}^2}$[/tex]) has 3 significant figures, so we should express the final answer with 3 significant figures as well:
[tex]\[
19.3 \frac{\text{newtons}}{\text{cm}^2}
\][/tex]
The pressure is [tex]\( 19.3 \frac{\text{newtons}}{\text{centimeter}^2} \)[/tex].
