Ok, that was pretty bassackwards. If anyone followed all that, I don't know whether to feel sorry for you, or commend you. Sorry to wast all that space. Wish I could edit, or even better delete...

Here is the "simple" way.....

Known equation from the data sheet:
Vout = Vs* (0.00369*P + 0.04)

using 1/271 = .00369, and dividing both sides by .00369

Vout * 271 = VS * (P + (.04/.00369))
or Vout * 271 = VS * (P + 10.84)

Vout * 271 / VS = P +10.84

(Vout * 271 / VS) - 10.84 = P

(Vout * (271 / 1023)) - 10.84 = P

(Vout * .2649) - 10.84 = P

But, again, the program that Alain pointed to in one of the above posts is useful to find a fraction to represent .00369.

Hopefully this is much cleaner to follow. It still yields the same result, just possibly less excedrin.