If you searched every square inch of your ultrabook and could not find the serial number, there’s an easier way to learn it.
Turn off the notebook and wait until it completely shuts down. Now turn it on again and quickly press the button to enter BIOS. Usually it is DEL, F2, F8 or similar to that, depending on the manufacturer. On the first page of the BIOS settings you will see the computer serial number. You’re sometimes required to present it when applying for repairs, and it is a good idea to write the number down beforehand, since it may be hard to launch BIOS on malfunctioning computer.
Beware, that letter O and digit 0 may look the same, so if your serial number has these symbols make sure to reference them against other symbols on screen, like the clock, to find out if it is a digit or a letter. When you’re done, select Discard changes and exit, confirm your selection and the computer will boot into operating system as usual.