The Correct Answer and Explanation is:
Of course. Here are the correct answers and detailed explanations for each problem.
4. How many weeks are equal to 3.94 x 10⁵ minutes?
Answer: Approximately 39.09 weeks
To solve this, we must convert minutes into weeks by setting up a chain of conversions. This process, often called dimensional analysis, involves multiplying by conversion factors until we arrive at the desired unit. First, we need to establish the relationships between the units: 60 minutes in an hour, 24 hours in a day, and 7 days in a week.
We can calculate the total number of minutes in one week:
60 minutes/hour × 24 hours/day × 7 days/week = 10,080 minutes/week
Now, we can convert the given number of minutes into weeks. The value 3.94 x 10⁵ is scientific notation for 394,000. To find the number of weeks, we divide the total minutes by the number of minutes in a single week:
394,000 minutes ÷ 10,080 minutes/week ≈ 39.087 weeks
Rounding to four significant figures, the answer is 39.09 weeks.
1. How many feet are equal to 25.57 dm?
Answer: Approximately 8.389 feet
This problem requires converting from a metric unit (decimeters, or dm) to an imperial unit (feet, or ft). A direct conversion factor is not commonly used, so it is easier to convert through a base unit like meters.
First, we convert decimeters to meters. The prefix “deci” means one-tenth, so there are 10 decimeters in 1 meter.
25.57 dm ÷ 10 dm/m = 2.557 meters
Next, we convert meters to feet. The standard conversion factor is that 1 meter is approximately equal to 3.28084 feet.
2.557 m × 3.28084 ft/m ≈ 8.3891 feet
The original measurement, 25.57 dm, has four significant figures. Therefore, we should round our final answer to four significant figures to maintain the same level of precision. This gives us a final answer of 8.389 feet.
6. The highest mountain in North America is Mt. McKinley at 2.048 miles high. How many kilometers is this?
Answer: Approximately 3.296 kilometers
To find the height of Mt. McKinley in kilometers, we need to convert the given value from miles to kilometers. This is a common conversion between the imperial and metric systems.
The key conversion factor is that 1 mile is approximately equal to 1.60934 kilometers. To perform the conversion, we multiply the height in miles by this factor.
2.048 miles × 1.60934 km/mile ≈ 3.29591872 kilometers
The given height, 2.048 miles, has four significant figures. It is standard practice to present the converted answer with the same number of significant figures as the original measurement. Rounding our result to four significant figures gives us 3.296.
Therefore, the height of Mt. McKinley is approximately 3.296 kilometers.
