To convert the speed of light from meters per second (m/s) to miles per hour (miles/h), we can use the following conversion factors:
- Meters to miles: 1 mile = 1609.34 meters
- Seconds to hours: 1 hour = 3600 seconds
Given the speed of light \( c \) in a vacuum is \( 2.998 \times 10^8 \) m/s, we can perform the conversion as follows:
\[ c \text{ (in miles/h)} = c \text{ (in m/s)} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \times \frac{3600 \text{ s}}{1 \text{ hour}} \]
Now substituting the values into the formula:
\[ c \text{ (in miles/h)} = 2.998 \times 10^8 \text{ m/s} \times \frac{3600 \text{ s}}{1 \text{ hour}} \times \frac{1 \text{ mile}}{1609.34 \text{ m}} \]
Calculating it step by step:
- Calculate \( \frac{3600}{1609.34} \):
\[ \frac{3600}{1609.34} \approx 2.237 \]
- Multiply this by \( 2.998 \times 10^8 \):
\[ c \text{ (in miles/h)} \approx 2.998 \times 10^8 \times 2.237 \approx 6.698 \times 10^8 \text{ miles/h} \]
Rounding to four significant digits gives:
\[ c \approx 6.698 \times 10^8 \text{ miles/h} \]
Thus, the speed of light in miles per hour, expressed to four significant digits, is:
\[ \boxed{6.698 \times 10^8} \text{ miles/h} \]