[tex]671080888\text{ }miles\text{ /hr}[/tex]
Explanation:
We are to convert from cm/sec to miles per hour
[tex]\text{Given: 3}\times10^{10}\text{ cm/sec}[/tex]
Using dimensional analysis:
We will break the conversion from cm to miles into smaller units:
from cm to meters, from meters to feet and from feet to miles
100cm = 1meter
0.3048 meters = 1 foot
5280 feet = 1 miles
From seconds to hour:
60 seconds = 1 minute
60 minutes = 1 hour
Let's start with the analysis from cm to miles:
[tex]\begin{gathered} 3\times10^{10}\text{ }\times\frac{cm}{\sec}\text{ = }3\times10^{10}\text{ }\times\frac{cm}{\sec}\times\frac{1\text{ meter}}{100\text{ cm}}\times\frac{1\text{ foot}}{0.3048\text{ meters}}\times\frac{1\text{ mile}}{5280\text{ f}eet} \\ =\text{ }3\times10^{10}\times\text{ }\frac{1}{160934.4}\times\frac{\text{miles}}{\sec} \\ =\text{ }\frac{3\times10^{10}}{160934.4}\times\frac{\text{miles}}{\sec} \end{gathered}[/tex]
Next we move to the analysis from seconds to hour:
[tex]\begin{gathered} \frac{3\times10^{10}\text{ }}{160934.4}\times\frac{miles}{\sec}\text{ = }\frac{3\times10^{10}\text{ }}{160934.4}\times\frac{miles}{\sec}\times\frac{60\text{ sec}}{1\text{ min}}\times\frac{60\text{ min}}{1\text{ hour}} \\ =\text{ }\frac{3\times10^{10}\text{ }}{160934.4}\times\frac{3600}{1}\times\frac{miles}{\text{hour}} \\ =\text{ }\frac{10800\times10^{10}\text{ }}{160934.4}\times\frac{miles}{\text{hour}} \end{gathered}[/tex][tex]\begin{gathered} =\text{ }671080888\times\frac{miles}{\text{hour}} \\ =\text{ }6.71080888\times10^8\frac{miles}{\text{hour}} \end{gathered}[/tex]
