To solve the problem of converting pressure from pounds per square inch to newtons per square centimeter, follow these steps:
1. Start with the given pressure:
The pressure inside the tire is given as [tex]\(28.0 \ \frac{\text{pounds}}{\text{inch}^2}\)[/tex].
2. Convert pounds to newtons:
We are given that [tex]\(1 \ \text{pound} = 4.45 \ \text{newtons}\)[/tex]. Therefore, multiply the given pressure by the conversion factor to change from pounds to newtons:
[tex]\[
28.0 \ \frac{\text{pounds}}{\text{inch}^2} \times 4.45 \ \frac{\text{newtons}}{\text{pound}}
\][/tex]
3. Convert inches squared to centimeters squared:
We are given that [tex]\(1 \ \text{inch}^2 = 6.45 \ \text{centimeters}^2\)[/tex]. To convert the area unit in the pressure measurement, we divide by the conversion factor:
[tex]\[
\frac{28.0 \ \text{pounds}}{\text{inch}^2} \times 4.45 \ \frac{\text{newtons}}{\text{pound}} \div 6.45 \ \frac{\text{centimeters}^2}{\text{inch}^2}
\][/tex]
4. Combine and simplify the units:
[tex]\[
\text{Pressure in newtons per centimeter}^2 = \frac{28.0 \times 4.45}{6.45} \ \frac{\text{newtons}}{\text{centimeter}^2}
\][/tex]
5. Calculate the numerical result:
Using the multiplications and divisions:
[tex]\[
= \frac{124.6}{6.45} \ \frac{\text{newtons}}{\text{centimeter}^2}
\][/tex]
[tex]\[
= 19.3 \ \frac{\text{newtons}}{\text{centimeter}^2}
\][/tex]
6. Rounding 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. The final answer should also be expressed with 3 significant figures.
The pressure is [tex]\( \boxed{19.3} \ \frac{\text{newtons}}{\text{centimeter}^2} \)[/tex].
