In the periodic table, the atomic mass of fluorine is given to 9 significant figures, whereas oxygen is given? WHy?

Oxygen is given what?

In my book the standard atomic weight of fluorine is given with ten significant figures. That's because there is only one stable isotope. All the other isotopes decay in less than 2 hours. One sample of pure fluorine is the same as any other sample of pure fluorine, as far as atomic weight goes.

Oxygen has three stable isotopes: O-16, O-17, and O-18. Any particular sample could have a different mix of these three, which makes the standard atomic weight of different samples vary from 15.99903 up to 15.99977. So it's useless to publish an atomic weight with more than 7 digits.
(Oxygen samples from air are pretty stable, at 15.999376. But oxygen from water, ice, or rock varies quite a bit.)

I've always assumed it's because we want to know exactly how much U235 is produced/consumed. Then again, maybe it is due to the fact that Fluorine has just one isotope meaning there can not be any natural variation.