DENSITY
Density is a ratio of mass to volume.
Mathematically speaking, D=m/v
 
TERM
DEFINITION
measured in the unit...
mass
amount of matter in a sample
gram
volume
space occupied by a sample
mL or cm3 (these equal each other)
density
ratio of a sample's mass to its volume
g/mL or g/cm3 (these equal each other)

How should you understand density?
Since students are always familiar with speed, I tell them that density is similar to speed.  Speed is also a ratio. It is a ratio of distance to time.


Here are densities for 3 substances:
SUBSTANCE
DENSITY
gold
19.3g/mL
water
1g/mL
styrofoam
.1g/mL
The density number means this: one milliliter of pure gold has mass = 19.3g
If you throw gold into water, since 19.3>1, it sinks.
Likewise, styrofoam floats because .1<1.

You can use the idea of density when you swim.  If you inhale and hold a bunch of air, it is easier to float because air has a very low density.
Maybe this will help... below are two pieces of bread.  They both have the same mass, but I squished one so its volume is smaller.

What happened when I threw them into water?

 
the big one floated
and the little one sank

Fish use a similar tactic.  They have an air bladder inside, and when they compress it (volume goes down) they sink more easily.  When they expand it (volume goes up) they float more easily.



SOME MATH
Since D=m/v, then m=D*v, and v=D/m
You cam use these equations when you know two variables and need to find the third.
For example, if D=.5g/mL and m=4g, then what is the volume of this sample?
v = D/m = (.5g/mL)/(4g) = .125mL (this could be something like styrofoam)(notice the "g" cancels)