Non-repeating decimals in 1/n

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Here's a conjecture I made: The number of non repeating decimal places in the base-ten representation of the fraction 1/n, where n is an integer, is equal to whichever is higher: the exponent of 2 in the prime factorization of n or the exponent of 5 in the prime factorization of n. Is this true? If so, how can I prove it?