You multiply the weight of the gem by the rate. For example, a diamond is 20 common coins per gram. Say you put a diamond on the scale, and it says 40 grams. 40grams*20coins per gram=800 common coins. And you do that for each gem weight/value.
I'm going to continue using 40grams just for reference. CPG means 'coins per gram'
40g diamond * 20 cpg = 800 coins
40g emerald * 10 cpg = 400 coins
40g ruby * 5 cpg = 200 coins
40g sapphire * 2 cpg = 80 coins
40g amethyst * 1 cpg = 40 coins
Just replace the 40g with whatever the weight of the gem is.