Select the statement that correctly characterizes the decimal representation of any irrational number.

The correct option is: It is non-terminating and non-repeating.

Explanation:

Real numbers are broadly categorized into rational numbers and irrational numbers based on their decimal expansions.

1. Rational Numbers: A rational number is any number that can be expressed as a fraction:

$\frac{p}{q}$

where $p$ and $q$ are integers, and $q\ne 0$. The decimal representation of a rational number is always either:
- Terminating: It comes to an end after a finite number of digits (e.g., $\frac{1}{4}=0.25$).
- Non-terminating and repeating: It continues infinitely but repeats a fixed sequence of digits (e.g., $\frac{1}{3}=\mathrm{0.333...}$).

2. Irrational Numbers: An irrational number cannot be expressed as a fraction of two integers. Because it cannot be written in fraction form, its decimal expansion goes on forever without ever establishing a repeating sequence or pattern.

Thus, the decimal representation of any irrational number is strictly non-terminating and non-repeating.

Standard mathematical examples of irrational numbers include:

$\sqrt{2}\approx \mathrm{1.41421356...}$

$\pi \approx \mathrm{3.14159265...}$