Why my swap-space is so low

I had a unable to find swap-on signature bug. So I searched & came onto this forum post.

http://sudan.ubuntuforums.com/showthread.php?t=381696

Seeing that did the following operations.

shirish@Mugglewille:~$ sudo mkswap -cv1 /dev/sdb3
[sudo] password for shirish:
Setting up swapspace version 1, size = 2056314 kB
no label, UUID=ddb44b87-2d55-4c5c-b06c-173da65a017c
shirish@Mugglewille:~$ sudo leafpad /etc/fstab
shirish@Mugglewille:~$ sudo swapon /dev/sdb3

Then just to check if the swap has been turned on or not did this.

shirish@Mugglewille:~$ free -m
            total used free shared buffers cached
Mem: 622 440 181 0 2 111
-/+ buffers/cache: 327 294
Swap: 1961 0 1961

Now this is where its starts to itch me. I have a /dev/sdb3 at 300 MiB/312 MB or thereabouts free but it never goes beyond this 1961, what is this 1961 ?

A cursory look at /dev/sdb3 gives this :-

shirish@Mugglewille:~$ df -h /dev/sdb3
Filesystem Size Used Avail Use% Mounted on
udev 312M 80K 312M 1% /dev

Why doesn't it use the rest?

Also there is something in the manual of mkswap which is bothering me.

To setup a swap file, it is necessary to create that file before initializing it with mkswap , e.g.
       using a command like

              # dd if=/dev/zero of=swapfile bs=1024 count=65536

       Note that a swap file must not contain any holes (so, using cp(1) to create the file is not accept‐
       able).

Now in our scenario above we haven't done that, would doing that make things easier? Also any idea if the bs & count should be same or should they be made any different?

Comments, suggestions all are welcome.