An irrational number is one that cannot be expressed as a simple fraction, and it has a non-repeating, non-terminating decimal expansion.
Let's analyze each option:
A. -9.121212121... is a repeating decimal (the digits "12" repeat), so it is a rational number. B. -5.690134489... appears to be non-repeating and terminating. Therefore, it can be expressed as a fraction, making it rational. C. -1.500000000... is a terminating decimal, which is also a rational number. D. -7.855555555... has the repeating part "5" at the end, so it is also a rational number.
Given this analysis, since all of the options provided are rational, none is an irrational number. However, if we are focusing strictly on non-terminating and what's most likely to be treated as irrational in a typical context, option A (-9.121212121...) is repeating but is still rational. But all options presented are rational. Would you like me to clarify something further?
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