To the whole gram is typically fine unless you have tiny babies. My scale measures to 0.1, but I never need anything measured that fine except spices. At something as fine as 0.01 gram, even air movement will disturb the reading. I would keep what you have unless you want something with more precision.
Generally, I would say it's trends of weight that you want to watch, less the specific number: Making sure young chams are gaining weight steadily, then once they plateau, you want to monitor for any sudden weight gain or drop. Even when my Ferds was acting totally normally and eating well, it was the slow and steady weight loss that let me know something was very wrong.