Question

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

Answer 1

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:

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

2. 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.**