# Question #e9714

Oct 24, 2016

Unit analysis is used to show that $1$ mile = $1.61$ km.

#### Explanation:

To show this relationship, we have to use several conversion factors. Some are within the standard measurement system, some are within the metric system, and one is the known conversion factor between the standard and metric systems:
$1$ mile = $5280$ feet
$1$ foot = $12$ inches

$1$ kilometer = $1000$ meters
$1$ meter = $100$ centimeters

$1$ inch = $2.54$ centimeters

$1$ mi * $5280$ ft/mi * $12$ in/ft * $2.54$ cm/in * $\frac{1}{100}$ m/cm * $\frac{1}{1000}$ km/m = $\frac{160934.4}{100000}$ km = $1.609344$ km $\approx 1.61$ km