Question

Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.
DIstance:
the distance from Santa maria to los alamos is 16.25 mi. what is the distance in cm?

Answer 1

To convert the distance from miles to centimeters, we can use dimensional analysis. We'll use the following conversion factors:

- 1 mile = 5280 feet
- 1 foot = 12 inches
- 1 inch = 2.54 centimeters

Now we can set up the conversion:

1. Start with the distance in miles:
\[
\text{Distance} = 16.25 \, \text{mi}
\]

2. Convert miles to feet:
\[
16.25 \, \text{mi} \times \frac{5280 \, \text{ft}}{1 \, \text{mi}} = \frac{16.25 \times 5280 \, \text{ft}}{1} = 85800 \, \text{ft}
\]

3. Convert feet to inches:
\[
85800 \, \text{ft} \times \frac{12 \, \text{in}}{1 \, \text{ft}} = \frac{85800 \times 12 \, \text{in}}{1} = 1029600 \, \text{in}
\]

4. Convert inches to centimeters:
\[
1029600 \, \text{in} \times \frac{2.54 \, \text{cm}}{1 \, \text{in}} = \frac{1029600 \times 2.54 \, \text{cm}}{1} = 2616214.4 \, \text{cm}
\]

Putting it all together, the distance from Santa Maria to Los Alamos in centimeters is:
\[
\text{Distance} = 2616214.4 \, \text{cm}
\]

Thus, the final answer is:
\[
\mathbf{2616214.4 \, cm}
\]