An irrational number is a number that cannot be expressed as a simple fraction (the ratio of two integers), and its decimal expansion is non-terminating and non-repeating.
-
Option A: 3.6363636363636363 is a repeating decimal (it can be expressed as \( \frac{109}{30} \)), which means it is a rational number.
-
Option B: 52.781654292 is a non-repeating, non-terminating decimal. Since it does not exhibit any repeating patterns, it is likely to be an irrational number.
Based on this analysis, the irrational option is B. 52.781654292.