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.

1 answer

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).