There are a few things that can cause gaps in your rings.
The angle is not correct on your saw. Make a sample ring from scrap wood and clamp, if you see gaps when you put the ring up to the light, make a minor adjustment to the angle and make another test ring until the gaps are gone.
Make sure that your saw blade is perpendicular to your cutting surface. If your saw is not finely tuned, inaccuracies can occur.
When gluing segments make sure that the tips of all segments are touching each other. If just one segment is not positioned accurately in the ring it will change its angle and a gap forms.
If you do a dry fit of the ring and see a gap, use the half ring approach.
If you have a hard time gluing all the segments at one time. Use a rub joint to glue segments in pairs. You then have less glue joints to deal with when you put it in the clamps.