What defines an irrational number?

An irrational number is defined as a real number that cannot be expressed as a simple fraction, which is characterized by non-terminating and non-repeating decimal expansions. This definition highlights that irrational numbers cannot be perfectly represented through the ratio of two integers, making them distinct from rational numbers.

For instance, well-known examples of irrational numbers include the square root of 2 and pi (π). These numbers cannot be expressed in fraction form, as their decimal representations continue indefinitely without repeating any sequence.

The other provided definitions do not accurately capture the essence of irrational numbers. For example, a number that can be expressed as a fraction describes rational numbers rather than irrational numbers. Whole numbers also don’t encompass the concept since many whole numbers (like 1, 2, or 3) are rational. Lastly, stating that a number is always negative does not pertain to irrational numbers, as irrational numbers can be both positive and negative, or even zero, where applicable.