If a number has decimal (4.10110111011110\ldots), what is it?

Irrational

A rational decimal either terminates or eventually repeats a fixed finite block of digits. An irrational decimal does neither: it continues indefinitely without settling into a permanent repeating cycle. The displayed digits are arranged with growing groups of ones between zeros, as in 1, 01, 011, 0111, and so on. The gaps and blocks keep changing, so no fixed block can describe the tail forever.

The decimal does not end, because more digits continue after those shown. It also is not eventually periodic: the lengths of the runs change rather than repeating with one fixed period. Therefore the number is non-terminating and non-recurring, which makes it irrational. Option B is correct. It cannot be an integer or a terminating decimal, and merely seeing a pattern does not make a decimal rational unless that pattern eventually repeats exactly.

This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Irrational numbers.