Since is an irrational number (see proof that e is irrational), it can not be represented as a fraction, but it can be represented as a continued fraction.
However, if an assertion were to be made about every irrational number, there would be no way to enumerate all the conjuncts, since irrationals can not be enumerated.
Being an irrational number, can not be expressed exactly as a common fraction, although fractions such as 22/7 and other rational numbers are commonly used to approximate.
Since the numerical value of an irrational number can not be stored exactly in a computer, an approximation of the incommensurate frequencies by all rational numbers is required in implementation.
An infinite continued fraction representation for an irrational number is useful because its initial segments provide rational approximations to the number.