A USD is worth somewhat less than 1 mg gold, according to the current spot price. Without active manipulation, the current equilibrium value is probably closer to 0.1 mg gold.
You're thinking of troy ounces. One ounce of gold is worth about $1226.00. There are 31.1034768 grams in a troy ounce, so a gram is worth about $39.42. A dollar is worth about 0.000815661 troy ounces or 0.025369883 grams of gold.