With the Lead Belly perk, you take 50% less radiation every time you drink from an irradiated water source. In Fallout: New Vegas, this benefit extends to all irradiated food and drink.
Because both games rely on the same engine as Oblivion, which used floating point numbers even if the player only saw rounded whole numbers, it is highly likely that a source of water that goes (for example) from "1 Rad" pre-perk to "1 Rad" post-perk is still accurately treated internally i.e. 1 Rad versus .5 Rad.
At high levels this perk may become redundant; RadAway, Rad-X, and apparel with radiation resistance, such as power armor, become more available and readily obtainable.