What type of numbers are included in the set of rational numbers?

The set of rational numbers encompasses all integers, fractions, and both terminating and repeating decimals. This is because a rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Integers, such as -3, 0, and 5, are included because they can be represented as fractions (for instance, -3 can be written as -3/1). Fractions, like 1/2 or -4/7, are inherently rational. Additionally, certain decimals are classified as rational; for example, 0.75 is a terminating decimal (which can also be expressed as 3/4), and 0.333... is a repeating decimal (which can be expressed as 1/3).

This understanding of rational numbers delineates them from other types of numbers, such as irrational numbers, which cannot be expressed in fraction form (like the square root of 2 or pi). Therefore, the inclusion of all integers, fractions, and specific types of decimals in the definition of rational numbers solidifies the correctness of this choice.