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Abstract.Redundancy in decimal-like representations of reals cannot be avoided. It is proved here that if {^,},=o,i,2,... is a countable collection of countable (or finite) sets of reals such that for each real x there are a¡ e A¡ with oo x *» ]T) a¡, (=0 then there is a dense subset of reals with redundant representations; that is, there is a dense set C of I such that for each x in C, x = S2^0a¡ and x = J2™0b¡ with a,, b¡ in A,-, but a, ^ b¡ for some i. Petkovsek [1] proved a similar result under the added assumption that every sum of the form SZ^rjOj with a¡i£ A¡ converges.

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