The atmospheric pressure is 700 mm Hg. What is the pressure in inches of Hg? (760 mm Hg = 29.92 in Hg) 26.7 in Hg 29.3 in Hg 15.3 in Hg 13.5 in Hg 27.6 in Hg
The Correct Answer and Explanation is:
To convert atmospheric pressure from mm Hg to inches of Hg, we use the conversion factor:760 mm Hg=29.92 in Hg760 \, \text{mm Hg} = 29.92 \, \text{in Hg}760mm Hg=29.92in Hg
Given that the atmospheric pressure is 700 mm Hg, we can set up the following proportion to convert it to inches of mercury:700 mm Hg760 mm Hg=x in Hg29.92 in Hg\frac{700 \, \text{mm Hg}}{760 \, \text{mm Hg}} = \frac{x \, \text{in Hg}}{29.92 \, \text{in Hg}}760mm Hg700mm Hg=29.92in Hgxin Hg
Now, solve for xxx:x=(700760)×29.92x = \left(\frac{700}{760}\right) \times 29.92x=(760700)×29.92
First, calculate the fraction:700760≈0.9211\frac{700}{760} \approx 0.9211760700≈0.9211
Now multiply by 29.92:x≈0.9211×29.92≈27.6 in Hgx \approx 0.9211 \times 29.92 \approx 27.6 \, \text{in Hg}x≈0.9211×29.92≈27.6in Hg
So, the atmospheric pressure in inches of mercury is approximately 27.6 in Hg.
Explanation:
- We started with the known conversion factor between mm Hg and inches of Hg (760 mm Hg = 29.92 in Hg).
- We then used a proportion to calculate the pressure in inches of Hg.
- The calculated result gives the pressure as 27.6 in Hg, which is the correct answer.
This kind of conversion is common in atmospheric pressure measurements, especially when comparing weather reports from different regions that use different units of pressure.
