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The pressure inside a tire is measured as 28.0 pounds/inch². What is its pressure in newtons/centimeter²?

1 pound = 4.45 newtons
1 inch² = 6.45 centimeters²

Express the answer to the correct number of significant figures.

The pressure is [tex]$\square$[/tex] newtons/centimeter².

Sagot :

GinnyAnswer
To convert the pressure from pounds per square inch to newtons per square centimeter, follow these detailed steps:

1. Identify the given values:
- Pressure: [tex]\(28.0 \frac{\text{pounds}}{\text{inch}^2}\)[/tex]
- Conversion factor: [tex]\(1 \text{ pound} = 4.45 \text{ newtons}\)[/tex]
- Conversion factor: [tex]\(1 \text{ inch}^2 = 6.45 \text{ centimeters}^2\)[/tex]

2. Convert pounds per square inch to newtons per square centimeter.

[tex]\[ \text{Pressure in } \frac{\text{newtons}}{\text{cm}^2} = 28.0 \frac{\text{pounds}}{\text{inch}^2} \times \frac{4.45 \text{ newtons}}{1 \text{ pound}} \times \frac{1 \text{ inch}^2}{6.45 \text{ cm}^2} \][/tex]

3. Perform the multiplication and division:

[tex]\[ 28.0 \times \frac{4.45}{6.45} = 28.0 \times 0.6899224806 \approx 19.318 \][/tex]

4. Round the result to the correct number of significant figures:
- The given pressure 28.0 has 3 significant figures.
- Therefore, we round 19.318 to 19.3 to maintain 3 significant figures.

The pressure is 19.3 [tex]\(\frac{\text{newtons}}{\text{centimeter}^2}\)[/tex].
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