To convert 31,350 feet (ft) to miles (mi) using dimensional analysis, we can utilize the provided conversion factor between feet and miles:

1 mile (mi) = 5280 feet (ft).

Step-by-Step Solution:

1. Start with the given quantity: $31,350 \, \text{ft}$

2. Set up a conversion factor to cancel out feet and convert to miles: $31,350 \, \text{ft} \times \frac{1 \, \text{mi}}{5280 \, \text{ft}}$

3. Perform the division: $= \frac{31,350}{5280} \, \text{mi}$

4. Calculate: $31,350 \div 5280 \approx 5.94 \, \text{mi}$

Answer:

$31,350 \, \text{ft} \approx 5.94 \, \text{mi}$

Would you like more details or have any questions?

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1. How would you convert miles to feet instead?
2. What if the distance was given in yards instead of feet?
3. How do we handle conversions with multiple steps in dimensional analysis?
4. How would you convert this distance to inches?
5. What are some real-world examples where dimensional analysis is used?

Tip: When doing dimensional analysis, always write out units explicitly to ensure they cancel correctly.