This unit conversion example problem demonstrates how to convert the speed of light in meters per second to miles per hour.

### Problem

The speed of light in a vacuum is 2.998 x 10^{8} m/sec. What is this speed in miles per hour?

### Solution

To convert this measurement, we need to convert meters to miles and seconds to hours. To do this, we need the following relationships:

1000 meter = 1 kilometer

1 kilometers = 0.621 mile

60 seconds = 1 minute

60 minutes = 1 hour

We can now set up the equation using these relationships so the units cancel out leaving only the desired miles/hour.

speed_{MPH} = 2.998 x 10^{8} m/sec x (1 km/1000 m) x (0.621 mi/1 km) x (60 sec/1 min) x (60 min/1 hr)

Note all the units cancelled out, leaving only miles/hr:

speed_{MPH} = (2.998 x 10^{8} x 1/1000 x 0.621 x 60 x 60) miles/hr

speed_{MPH} = 6.702 x 10^{8} miles/hr

### Answer

The speed of light in miles per hour is 6.702 x 10^{8} miles/hr.