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Despite using an irrational number base, when using standard form, all non-negative integers have a unique representation as a terminating ( finite ) base-φ expansion.
Other numbers have standard representations in base-φ, with rational numbers having recurring representations.
These representations are unique, except that numbers with a terminating expansion also have a non-terminating expansion, as they do in base-10 ; for example, 1 = 0. 99999 ….

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