A body floats when the buoyant force on its submerged part exactly balances its weight, so the residual net force closes at zero and it neither sinks nor rises. That threshold is exact only for a stated fluid density, displaced volume, gravity, static equilibrium, and simple geometry. Real floating bodies add shape, wetting, density variation, scale calibration, surface motion, and uncertainty.
A toy floating threshold is a zero-residual force ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.