Arocket speed is 2 1/3 miles per second. how fast is this in miles per hour?

(2 1/3 miles/sec)*(3600 sec/hr) = 8400 mph . . . this is just using dimensional analysis to convert units

You can solve this by setting up ratios that when cross-multiplied cancel out the units.  For example, having a value with a unit of miles in the numerator and seconds in the denominator multiplied by a value with a unit of seconds in the numerator and minutes in the denominator would cancel out the seconds and leave you with a ratio of miles over minutes.

*You can convert seconds to minutes (if seconds was on the bottom of a fraction) by multiplying by the number of seconds in a minute over one minute.*

Multiply the numerators and denominators separately, cross out canceled units, and simplify if needed.  "Crossed out" units are in italics.  Units that are kept are in bold.

2+(1/3) miles  x  60 seconds  x  60 minutes  =  8400 miles
1 second             1 minute           1 hour               1 hour

8400 miles per hour