Answer:
The correct option is;
0.100100010000...
Explanation:
An irrational number in mathematics are the subset of real numbers that are not rational numbers such as √2, π, e. As such it is not possible to express an irrational number as a ratio of two integers, or expressed in the form of a simple fraction.
The decimal portion of the expression of an irrational number are non periodic and they do not terminate. Transcendental, which are non algebraic, numbers are all irrational numbers
In the question, the number 0.100100010000... has non terminating non recurring decimals and is therefore an irrational number.