Ubuntu says my disk is full when installing updates but is not

Question

I'm trying to install updates on an Ubuntu Server but it keeps telling me that there is no space, here is my df -h output:

root@ServerMonitor:/# df -h
S.ficheros     Tamaño Usados  Disp Uso% Montado en
udev             486M   4,0K  486M   1% /dev
tmpfs            100M   504K   99M   1% /run
/dev/sda1         23G    17G  5,0G  77% /
none             4,0K      0  4,0K   0% /sys/fs/cgroup
none             5,0M      0  5,0M   0% /run/lock
none             497M      0  497M   0% /run/shm
none             100M      0  100M   0% /run/user

What should I do?

Thanks

EDIT:

The output for df -i shows100% for /, how do I solve it?

root@ServerMonitor:/# df -i
S.ficheros     Nodos-i NUsados NLibres NUso% Montado en
udev            124415     421  123994    1% /dev
tmpfs           127221     373  126848    1% /run
/dev/sda1      1507328 1503606    3722  100% /
none            127221       2  127219    1% /sys/fs/cgroup
none            127221       4  127217    1% /run/lock
none            127221       1  127220    1% /run/shm
none            127221       2  127219    1% /run/user