There are a total of 8 rectangular tables with 6 chairs each, so the total number of rectangular chairs is 8 x 6 = <<8*6=48>>48 chairs.
There are also 5 round tables with 4 chairs each, so the total number of round chairs is 5 x 4 = <<5*4=20>>20 chairs.
The total number of chairs in the community center is 48 + 20 = <<48+20=68>>68 chairs.
Since the chairs are randomly numbered and the freshman will be randomly assigned a seat number, the probability that the first freshman to arrive will be seated at a round table is the ratio of the number of round chairs to the total number of chairs, which is 20/68 = <<20/68=0.2941>>0.2941, or 29.41%. Answer: \boxed{0.2941}.