# If a number is irrational, then does its mantissa contain every possible digit sequence of finite length?

For a number to be irrational, it must be impossible to express the value as a ratio of integers. So, if I look at the infinite string of digits to the right of the number's decimal point, can I find any given integer sequence of length n (n natural), or is that not guaranteed?

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You're not even guaranteed to find any given digit. For example, $0.110100100010000...$. –  Qiaochu Yuan Aug 4 '11 at 1:58

It is not guaranteed. For example, $0.101001000100001...$ is irrational. A number is rational if and only if its decimal expansion either terminates or from some point on repeats, so any non-terminating decimal that doesn’t end in an infinite string of repetitions of a single finite block of digits must represent an irrational number.
No. Consider e.g. $.1101001000100001\ldots$.