Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.

DIstance:
how man inches are in 10,000 miles

1 answer

To convert miles to inches using dimensional analysis, we can use the following conversion factors:

  1. There are 5,280 feet in a mile.
  2. 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:

  1. Convert miles to feet:

\[ 10,000 , \text{miles} \times \frac{5,280 , \text{feet}}{1 , \text{mile}} = 52,800,000 , \text{feet} \]

  1. 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.