Describing a decimal number where one or more digits repeat infinitely in a pattern, often shown with a bar over the repeating digits. Examples include 0.333... (written as 0.3̄) or 0.142857142857... (written as 0.142857̄).
From Latin 'repetere' meaning 'to seek again' or 'to do again'. The mathematical concept of repeating decimals was formalized during the development of decimal notation in the 16th and 17th centuries, though the phenomenon was observed much earlier.
Repeating decimals reveal a beautiful truth: every fraction creates either a terminating or repeating decimal, never anything random! This happens because division is essentially controlled - when you run out of new remainders, you must start repeating, creating these elegant infinite patterns.
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