Let's say you had a speed given in miles per hour and had to convert it to meters per second...

THE PROBLEM:

I teach students how to use dimensional analysis to solve problems like this.
To use this method, you start out with what you were given, but write it clearly, like this...

This is just another way of writing 60mi/Hr (actually it's exactly the same, just easier to see)

Next, we fix distance.  I mean that we were given miles as a distance unit, but we want meters.


We must multiply by a fraction that has miles on the bottom since we were given miles on top.
This way we can cancel out miles as a unit, and be left with meters.

Next we fix time.  Like with distance, this time we need Hours on top and seconds on bottom...
so we add another fraction...


Now all we have to do is put numbers in our fractions so that the tops equal the bottoms... like this:
we are told that 1mi=1609m and that 1Hr=3600s, so we fill them in...
 


Now all we have to do is multiply across the top then divide by whatever is on the bottom...
60*1609/3600 and that's it!

What's the answer?

26.8 What?  Well, whatever units are on both top and bottom get cancelled out, so all we have left is...