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To convert the pressure from pounds per square inch ([tex]$\frac{\text{lb}}{\text{in}^2}$[/tex]) to newtons per square centimeter ([tex]$\frac{\text{N}}{\text{cm}^2}$[/tex]), follow these steps:
1. Start with the given pressure in pounds per square inch:
[tex]\[ 28.0 \frac{\text{lb}}{\text{in}^2} \][/tex]
2. Convert pounds to newtons:
[tex]\[ 1 \text{ lb} = 4.45 \text{ N} \][/tex]
Therefore,
[tex]\[ 28.0 \frac{\text{lb}}{\text{in}^2} \times 4.45 \frac{\text{N}}{\text{lb}} \][/tex]
3. Convert square inches to square centimeters:
[tex]\[ 1 \text{ in}^2 = 6.45 \text{ cm}^2 \][/tex]
Therefore,
[tex]\[ 28.0 \left( \frac{\text{lb}}{\text{in}^2} \times 4.45 \right) / 6.45 \][/tex]
4. Calculate the intermediate value:
[tex]\[ 28.0 \times 4.45 = 124.6 \text{ N/in}^2 \][/tex]
Now divide by 6.45 to convert to [tex]$\text{N/cm}^2$[/tex]:
[tex]\[ \frac{124.6}{6.45} = 19.318 \text{ N/cm}^2 \][/tex]
5. Express the answer to the correct number of significant figures:
- The initial value (28.0) has 3 significant figures.
- Therefore, the final answer should also have 3 significant figures.
Hence, the pressure is:
[tex]\[ \boxed{19.318} \frac{\text{newtons}}{\text{centimeter}^2} \][/tex]
1. Start with the given pressure in pounds per square inch:
[tex]\[ 28.0 \frac{\text{lb}}{\text{in}^2} \][/tex]
2. Convert pounds to newtons:
[tex]\[ 1 \text{ lb} = 4.45 \text{ N} \][/tex]
Therefore,
[tex]\[ 28.0 \frac{\text{lb}}{\text{in}^2} \times 4.45 \frac{\text{N}}{\text{lb}} \][/tex]
3. Convert square inches to square centimeters:
[tex]\[ 1 \text{ in}^2 = 6.45 \text{ cm}^2 \][/tex]
Therefore,
[tex]\[ 28.0 \left( \frac{\text{lb}}{\text{in}^2} \times 4.45 \right) / 6.45 \][/tex]
4. Calculate the intermediate value:
[tex]\[ 28.0 \times 4.45 = 124.6 \text{ N/in}^2 \][/tex]
Now divide by 6.45 to convert to [tex]$\text{N/cm}^2$[/tex]:
[tex]\[ \frac{124.6}{6.45} = 19.318 \text{ N/cm}^2 \][/tex]
5. Express the answer to the correct number of significant figures:
- The initial value (28.0) has 3 significant figures.
- Therefore, the final answer should also have 3 significant figures.
Hence, the pressure is:
[tex]\[ \boxed{19.318} \frac{\text{newtons}}{\text{centimeter}^2} \][/tex]
Answer:
Explanation:
To convert the pressure from pounds per square inch ($\frac{\text{lb}}{\text{in}^2}$) to newtons per square centimeter ($\frac{\text{N}}{\text{cm}^2}$), follow these steps:
1. Start with the given pressure in pounds per square inch:
\[
28.0 \frac{\text{lb}}{\text{in}^2}
\]
2. Convert pounds to newtons:
\[
1 \text{ lb} = 4.45 \text{ N}
\]
Therefore,
\[
28.0 \frac{\text{lb}}{\text{in}^2} * 4.45 \frac{\text{N}}{\text{lb}}
\]
3. Convert square inches to square centimeters:
\[
1 \text{ in}^2 = 6.45 \text{ cm}^2
\]
Therefore,
\[
28.0 \left( \frac{\text{lb}}{\text{in}^2} * 4.45 \right) / 6.45
\]
4. Calculate the intermediate value:
\[
28.0 * 4.45 = 124.6 \text{ N/in}^2
\]
Now divide by 6.45 to convert to $\text{N/cm}^2$:
\[
(124.6)/(6.45) = 19.318 \text{ N/cm}^2
\]
5. Express the answer to the correct number of significant figures:
- The initial value (28.0) has 3 significant figures.
- Therefore, the final answer should also have 3 significant figures.
Hence, the pressure is:
\[
\boxed{19.318} \frac{\text{newtons}}{\text{centimeter}^2}
\]
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