A floating point system and method employing instructions where instruction have incorporated floating point information. The floating point information indicates whether an exception trap should occur and the type of rounding to be performed upon "inexact" arithmetic results. The floating point information further indicates whether other floating-point exception traps should occur. This information allows dynamic (e.g. instruction-by-instruction) modification of various operating parameters of the CPU without modifying information in status registers using special instructions or modes, thereby increasing overall CPU performance. The technique is also supported by several mechanisms for providing precise floating-point exceptions.