The problem i see is this:
I do not see 10gb anywhere.
Your rootfs is 3gb, your home is inside those 3gb.
So anything else but a console OS is not possible to work flawlessy.
By that i think of: If you have copied just 1 movie, or your favorite cd ripped as mp3 (or ogg), by just that action you used another 1 gb.
If you're using the internet, or even youtube, you can quickly raise the temp (eg. ~/.cache) folder size rapidly with garbage either.
To verify and get more hints, whats the output of:
I'm posting from windows and its very late here, it might be "-p" instead of "-l".
Either way, if i had 10gb to install a linux on, i'd use as this:
/boot ext4 384mb
swap swap 768mb
/home ext4 2048mb
/ ext4 7040mb
Keep in mind, that is still VERY minimalistic!