Why should monetary values always be stored as NUMERIC rather than REAL or FLOAT?

NUMERIC stores digits directly in an exact, arbitrary-precision base-10 representation. REAL/DOUBLE PRECISION store values in IEEE 754 binary floating point, which cannot represent most decimal fractions exactly — 0.10 is actually stored as a close binary approximation. For money, these tiny, silent rounding errors compound across enough transactions into a real, visible discrepancy.