Computing a function on natural numbers assumes a fixed notation for natural numbers. Usually, we assume the binary or decimal notation. However, different notations might have different sets of effectively (PTIME) computable functions. We compare notations with respect to the set of effectively computable functions under a given notation. This approach gives an inclusion based partial ordering on notations, say ≤PTIME. We address the question whether the binary notation is, in some way, distinguished. We say that a notation σ is dense if the length of a σ-numeral for n is a function bounded by poly(log⁡(n+1)). We show that the binary notation is a maximal element in ≤PTIME among dense notations. We also show that a dense notation σ allows to compute effectively a different set of functions than the binary notation only if σ has short numerals for large numbers. •Among all dense notations for natural numbers, positional notations allow to compute in PTIME a maximal set of functions.•Any dense notation computing in PTIME all functions computable under the binary notation is PTIME isomorphic with the binary one.•Any dense notation computing in PTIME a function not computable in PTIME under the binary notation codes some numbers with short codes.