ACTA ARITHMETICA

On decimal and continued fraction expansions of a real number by C. Faivre (Marseille) 0. Introduction. Let x be an irrational number. We deal with the problem of finding from the decimal expansion of x, the first k (where k is a given integer) partial quotients of the regular continued fraction expansion of x. More precisely, for each n ≥ 1, denote by xn, yn with xn < x < yn the two consecutive nth decimal approximations of x. We assume that th