Question

Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.
DIstance:
How many miles will a person run during a 10-kilometer race.

Answer 1

To convert kilometers to miles using dimensional analysis, we need to start with the known distance in kilometers and use a conversion factor.

The given data for the problem:

- Distance of the race: \(10 \text{ kilometers}\)

**Step 1: Write down the distance in kilometers.**

\[
10 \text{ km}
\]

**Step 2: Use the conversion factor to convert kilometers to miles.**

The conversion factor between kilometers and miles is:

\[
1 \text{ kilometer} = 0.621371 \text{ miles}
\]

**Step 3: Set up the dimensional analysis.**

We want to multiply the distance in kilometers by the conversion factor:

\[
10 \text{ km} \times \frac{0.621371 \text{ miles}}{1 \text{ km}}
\]

**Step 4: Cancel the units and perform the multiplication.**

The kilometers cancel out:

\[
10 \times 0.621371 \text{ miles} = 6.21371 \text{ miles}
\]

**Step 5: Final Answer.**

Thus, the person will run approximately

\[
\boxed{6.21 \text{ miles}}
\]

during a 10-kilometer race (rounded to two decimal places).