To determine which of the given numbers is irrational, let's briefly evaluate each option:
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0.11111111... - This is a repeating decimal, which can be expressed as the fraction 1/9. Therefore, it is a rational number.
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-4.1297 - This number is a terminating decimal and can be expressed as a fraction, so it is rational.
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0.123451234512345... - This number has a repeating pattern (the sequence "12345"), making it a rational number as well.
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4/27 - This is a fraction, and it is therefore rational.
Since all options listed are rational, none of them represent an irrational number. However, an irrational number is one that cannot be expressed as a simple fraction; examples include numbers like \(\sqrt{2}\) or \(\pi\).
If we must choose from these options and are given the premise of identifying an irrational number, it appears there may be a misunderstanding in the provided options, as none of them is irrational.