Chapter 6.5, Problem 50SR

To determine

To complete the given conversion.

Answer to Problem 50SR

10 kilometres is approximately 6.21 miles.

Explanation of Solution

Given information:

The given conversion is

  $10\text{km}\approx \text{mi}$

Calculation:

Dimensional analysis is the process of including units of measurement as factors when you compute. For example, you know that $1\text{hour=60}\text{minutes}$ .

Each ratio is equivalent to 1 because the numerator and denominator represent the same amount.

To convert 10 kilometres into miles as follows:

Use $1\text{km}\approx \text{0}\text{.621}\text{mi}$ .

  $\begin{array}{c}10\text{km}\approx \text{10}\text{km}·\frac{0.621\text{mi}}{1\text{km}}\text{multiply}\text{by}\frac{0.621\text{mi}}{1\text{km}}\\ 10\text{km}\approx \text{10}\cancel{\text{km}}·\frac{0.621\text{mi}}{1\cancel{\text{km}}}\text{Divide}\text{out}\text{common}\text{units,}\text{leaving}\text{the}\text{desired}\text{unit,mi}\text{.}\\ \text{10}\text{km}\approx \text{6}\text{.21}\text{mi}\text{Simplify}\end{array}$

So, 10 kilometres is approximately 6.21 miles.