The F (major) Chord is played as a barre at the first fret- in the "open" position- thus:
e-1
b-1
g-1
d-2
a-3
E-3
E being the low e string. Think of it as an e (major) chord "slid up one" :)
This is because this positions give the lowest notes for an F on a fretboard.
The other (easy) position for an F maj is the same chord at fret 13 - octave higher.
Accuracy,you say? hmm interesting concept..