Question

Which of the following is irrational?

• A. $0.14$
• B. $0.14\overline{16}$
• C. $0.\overline{1416}$
• D. $0.1014001410014\cdots$

Answer 1

The correct option is D $0.1014001410014\cdots$

An irrational number cannot be represented in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$.

A non-terminating and non-recurring decimal cannot be represented in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$.
Hence, an irrational number is non-terminating and non-recurring decimal.

So, 0.1014001410014... is an irrational number since it is non-terminating and non- recurring.