Which of the following best describes irrational numbers?

Irrational numbers are defined as those real numbers that cannot be expressed as simple fractions. This means they cannot be represented as a quotient of two integers, which is a key characteristic that distinguishes them from rational numbers. Instead, irrational numbers have decimal expansions that are non-repeating and non-terminating.

The fact that an irrational number is continuous but not repeating is fundamental because it highlights their nature as numbers that extend infinitely without falling back on a repeating pattern. For example, the square root of 2 or pi (π) are classic examples of irrational numbers because their decimal representations go on forever without repetition.

Other choices do not accurately encompass the nature of irrational numbers. While it is true that irrational numbers can be represented on the number line, this statement applies to all real numbers, not just irrational numbers. The ability to express numbers as fractions is exclusive to rational numbers, and numbers with exact decimal forms refer to rational numbers that terminate or repeat. Thus, the defining characteristic of irrational numbers is their non-repeating and non-terminating decimal representation, confirming that the best description is that they are continuous but not repeating.