What defines an irrational number?

An irrational number is defined by its inability to be expressed as a simple fraction or a ratio of two integers. Specifically, irrational numbers include non-terminating, non-repeating decimals, which means they go on infinitely without forming a repeating pattern. An example of this is π (pi), which is approximately 3.14159, and its decimal representation continues indefinitely without repeating.

The reason option B is the correct answer lies in its inclusion of both pi and non-terminating decimals as key examples of irrational numbers. These types of numbers are fundamentally different from rational numbers, which can be represented as fractions, such as 1/2 or 3/4, and may either terminate (like 0.5) or repeat (like 0.333...).

In contrast, repeating decimals indicate rational numbers because they can be expressed as a fraction. Integers are a subset of rational numbers as they can be written as fractions (e.g., 5 can be represented as 5/1). All fractions, by definition, consist of rational numbers, encompassing both whole numbers and decimals that either terminate or repeat. Thus, they do not fit the definition of irrational numbers.

This understanding helps clarify why option B effectively captures the essence