Three decimals should be enough for any of today's tiers.
It comes down to the division of strokes by games to calculate the average, games being the no. of games in question, and strokes being the sum of strokes of these games.
The games no. is limited by the "saturation" no. of each tier. The lower tiers have a max. of 50 (Tour Master) which gives 1/50 = 0.02 as the lowest increment. Until there, two digits are sufficient.
Legend comes with 1 / 500 = 0.002 increment,
Tour Legend has 1 / 750 = 0.00133...,
Champion has 1 / 1000 = 0,001
(Tour Champion doesn't have a saturation no. yet)
That said, any three decimal average notation will be able to distinguish between "below the threshold" and "arrived at/surpassed threshold" for tier promotion.