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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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How do you calculate/prove the length of n, the number of non-repeating digits preceeding a ... [closed]

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example: 1/6 = 0.1666.... (there is 1 non repeating digit) **( …
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