Another example is the density of water. The density of water at ``standard
temperature and pressure'', is 
(i.e. 
).
What is the density of water in SI units, which would be 
? To do this,
you need to realize that one kilo gram = 1000 grams, and
1 m = 100 centimeters. So putting this together means that
When you work with lots of equations, one easy way to get the
wrong answer is to mess up with the units. Lets do an example.
What is the mass of a sphere of water of radius 1 cm?
Well eq. 2.1 tells us that the
mass 
. What is V? You might recall that
the volume of a sphere is 
, where here
the radius r = 1cm. So we have
So what do we do now? Plug and chug! Take the value of the density
and the radius r = 1cm and plug it in.
So what'll we get?
4189 what??? Is the answer kilograms, grams, or what? It better not be kilograms because our intuition should tell us that a sphere of water that size could not be anything like that much mass! What we did was very sloppy and gave us the wrong answer !!. To do this the right way, we need to put in the units. Mass and length aren't just numbers, they have units also. So what is really the correct way to do this is to say
Then we need conversion between cm and m which is 1m = 100 cm. This gives
Alternatively we could have been consistent and have done the whole
thing using SI units. So we would write 
, which is
in SI units. So now
Notice that the units of 
cancel out leaving the units of kg.
This is the correct units. If instead we had obtained the units 
,
then we would have had to have made a mistake some place. This shows the
importance of always checking units.
