We find the minimal information cost me(ε) of obtaining an ε–approximation of a linear problem, assuming that available information consists of noisy (perturbed) values I of linear functionals: Perturbations can be absolute or relative, and are assumed to be bounded, each bound dependent on a consecutive number of a functional. We determine the optimal (up to a constant) number of functionals, optimal precisions with which they should be obtained, as well as the best information and algorithm. The results are applied to the problem of recovering functions in s variables withrcontinuous derivatives, where noisy information is given by function values represented in finite precision arithmetic. The minimal cost, measured by the number of binary bits sufficient for representing information from which the εapproximation can be obtained, is then proportional to.