The speed of light in a vacuum is \(2.998 \times 10^{8} \mathrm{~m} / \mathrm{s}\). What is its speed in (a) \(\mathrm{km} / \mathrm{h} ;\) (b) \(\mathrm{mi} / \mathrm{min} ?\)

Unit conversion is a vital skill in science and engineering. It helps to transform values from one system of units to another for better understanding and communication. Consider different units like meters per second (m/s) and the need to convert it to kilometers per hour (km/h) or miles per minute (mi/min). Conversions typically involve multiplying by conversion factors. A conversion factor is a ratio that expresses how many of one unit are equal to another unit.

Always confirm the conversion factors first. For instance, 1 kilometer equals 1000 meters, and 1 hour equals 3600 seconds. This will help you in doing precise calculations. The same principle applies when converting meters to miles, where 1 mile equals 1609.34 meters.

Converting units simplifies comparing and interpreting physical quantities measured in different systems.

To convert meters per second (m/s) to kilometers per hour (km/h), start by understanding the base units. One kilometer is equal to 1000 meters, and one hour equals 3600 seconds.

First, convert meters to kilometers by using the factor: 1 km = 1000 m. Thus, you divide the speed in m/s by 1000. For example, the speed of light is given as 2.998 x 10\textsuperscript{8} m/s. Converting this to kilometers per second gives: \[ 2.998 \times 10^{8} \times \frac{1}{1000} = 2.998 \times 10^{5} \text{ km/s} \]

Next, convert seconds to hours using the factor: 1 hour = 3600 seconds. Multiplying by 3600 converts the result into kilometers per hour: \[ 2.998 \times 10^{5} \times 3600 = 1.07928 \times 10^{9} \text{ km/h} \]

This ensures your speed value is now scaled appropriately to kilometers per hour. This process brings consistency in everyday contexts where travel speeds are generally measured in km/h.

To convert meters per second (m/s) to miles per minute (mi/min), identify the necessary conversion factors. There are 1609.34 meters in one mile and 60 seconds in a minute.

Start by converting meters to miles. For instance, take the speed of light at 2.998 x 10\textsuperscript{8} m/s. By converting meters to miles using the factor: 1 mile = 1609.34 meters, you divide the speed by 1609.34: \[ 2.998 \times 10^{8} \times \frac{1}{1609.34} = 1.86412 \times 10^{5} \text{ mi/s} \]

Finally, convert seconds to minutes. Since 1 minute equals 60 seconds, multiply the result by 60 to convert mi/s to mi/min: \[ 1.86412 \times 10^{5} \times 60 = 1.11847 \times 10^{7} \text{ mi/min} \]

This conversion is vital for understanding speeds in contexts familiar to different regions, such as in countries using miles for road distances.