In mathematics, the repeating decimal **0.999...** (sometimes written with more or fewer 9s before the final ellipsis, or as **0.9**, **0.(9)**, or ) denotes a real number that can be shown to be the number one. In other words, the symbols "0.999..." and "1" represent the same number. Proofs of this equality have been formulated with varying degrees of mathematical rigor, taking into account preferred development of the real numbers, background assumptions, historical context, and target audience.

Every nonzero, terminating decimal has an equal twin representation with infinitely many trailing 9s, such as 8.32 and 8.31999... The terminating decimal representation is almost always preferred, contributing to the misconception that it is the only representation. The same phenomenon occurs in all other bases or in any similar representation of the real numbers.