  The Operator axioms have produced new real numbers with new operators. New
operators naturally produce new equations and thus extend the traditional
mathematical models which are selected to describe various scientific rules. So
new operators help to describe complex scientific rules which are difficult
described by traditional equations and have an enormous application potential.
As to the equations including new operators, engineering computation often need
the approximate solutions reflecting an intuitive order relation and
equivalence relation. However, the order relation and equivalence relation of
real numbers are not as intuitive as those of base-b expansions. Thus, this
paper introduces numerical computations to approximate all real numbers with
base-b expansions.
