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).
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