Note that this property of decimal expansions means it's impossible to effectively identify computable real numbers defined in terms of a decimal expansion and those defined in the formula_25 approximation sense. Hirst has shown there is no algorithm which takes as input the description of a Turing machine which produces formula_25 approximations for the computable number "a", and produces as output a Turing machine which enumerates the digits of "a" in the sense of Turing's definition (see Hirst 2007). Similarly it means that the arithmetic operations on the computable reals are not effective on their decimal representations as when adding decimal numbers, in order to produce one digit it may be necessary to look arbitrarily far to the right to determine if there is a carry to the current location. This lack of uniformity is one reason that the contemporary definition of computable numbers uses formula_25 approximations rather than decimal expansions.