To convert miles to inches using dimensional analysis, we can use the following conversion factors:
- There are 5,280 feet in a mile.
- There are 12 inches in a foot.
Starting with 10,000 miles, we can set up the conversion using these factors.
\[ 10,000 , \text{miles} \times \frac{5,280 , \text{feet}}{1 , \text{mile}} \times \frac{12 , \text{inches}}{1 , \text{foot}} \]
Now, perform the calculations step by step:
- Convert miles to feet:
\[ 10,000 , \text{miles} \times \frac{5,280 , \text{feet}}{1 , \text{mile}} = 52,800,000 , \text{feet} \]
- Convert feet to inches:
\[ 52,800,000 , \text{feet} \times \frac{12 , \text{inches}}{1 , \text{foot}} = 633,600,000 , \text{inches} \]
So, the final result is:
\[ 10,000 , \text{miles} = 633,600,000 , \text{inches} \]
Thus, there are 633,600,000 inches in 10,000 miles.