To find the total weight of the ring, add the weight of the center stone, the baguettes, and the round brilliants. The center stone weighs 0.83 ct, the two baguettes weigh 0.10 ct each (totaling 0.20 ct), and the six round brilliants weigh 0.02 ct each (totaling 0.12 ct). Therefore, the total weight is 0.83 ct + 0.20 ct + 0.12 ct = 1.15 ct.