Nose numbers are located below the cockpit, under the cheatline - roughly half way between the cheatline and the nosewheel area. Anyway it's the only number there so you can't miss it. Sometimes it's also got an ETOPS marker (on a twin, obviously) if that's applicable.

The "take out the 2nd digit from the fleet / nose number" trick is generally OK, but not in all cases since the fleet numbers (first 2 digits) don't always match reality (eg: 8107, = N107UA, but 2366 = N766UA). It's basically the last 2 digits plus knowing the tail number registrations for each fleet (eg: 777's are N7xxUA *and* N2xxUA, 737's are N3xxUA & N9xxUA) so they don't always match up.

Just for interest with the 2nd digit - that refers to what I call the cabin configuration version number, or plane type -this is most useful when a fleet is undergoing upgrade like a seat swap or something - those numbers can tell you if you will get a nasty surprise on the inside or not.

Referring to the earlier question about the 744 OB's, OA's & OP's... my distorted memory suggests that the OA's (the high density equipment w/80? C, 270Y) were 80xx and the OP's (the low density pacific config) were 83xx's - though I could be wrong on that.

I have more info on this at home I'll try and scrounge it up.