AbstractFor any fixed positive real number ε, any integerb≥2 and anydε{0, 1,…, b−1}, the set of Borel's simply normal numbers to basebin [0, 1] is partitioned into a countable number of sets in eight different ways according to the largest place and the number of places at which the proportiond's to that place in theb‐adic expansion of such a number exceeds or is not less thanb−1– ε, or is less than or does not exceedb−1– ε. For selected values ε, the Lebesgue measures of the sets in these decompositions are given explicitly.