"Do i have to format only system partition or do i have to format the whole hard disk?"
You would only have to re-initialize the "boot partition". No need to re-initialize and re-partition the entire drive.
As mentioned in reply #2, you should consider some kind of external backup.
I DO NOT recommend using Time Machine, however.
Instead, get an external drive with an overall capacity larger than the total of your internal (that is, 250gb or larger).
Then, partition it, just as you did your internal drive.
Next, download CarbonCopyCloner (or Superduper). You can get CCC here:
http://www.bombich.com/download.html
Now, use CCC to "clone" your internal boot partition (to your EXTERNAL boot partition) and then your internal data patition (to your EXTERNAL data partition).
Do this, and you will be fully protected against a failure of the internal drive.
A CCC backup is BOOTABLE and is also in POFF (plain ol' finder format) -- just mount it and "go". You CAN'T BOOT from a T.M. backup.
You can either buy an external drive, but I actually suggest you purchase the drive "core" and enclosure separately, and build it yourself. It's easy to do, and since you put it together, if anything ever goes wrong with it, you'll know how to take it apart.
I suggest this as an enclosure:
http://oyendigital.com/hard-drives/store/U32-M.html
Then find a 2.5" drive to go inside...