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

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

• A. Only whole numbers and irrational numbers
• B. Only integers
• C. All integers, fractions, and terminating or repeating decimals
• D. Only positive integers

Answer: (C)

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.

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.