Expanded notation is the term given in elementary mathematics education for the expansion of a positive integer in the form sum_k b_k 10^k, i.e., as a sum of appropriate powers of 10 (the base of the expansion) times its digits (in the case of base-10, decimal digits). For example, the number with decimal expansion 1234 would be written in expanded form as 1234 = 1×1000 + 2×100 + 3×10 + 4. Negative k are also allowed in expanded notation of arbitrary (not necessarily integer) numbers, e.g., 1234.56 = 1×1000 + 2×100 + 3×10 + 4 + 5×1/10 + 6×1/100, but such expansions usually not considered or deferred in elementary education contexts.

base | decimal expansion | engineering notation | scientific notation