Yes, every integer is indeed considered a rational number. To understand why, let’s start by defining what integers and rational numbers are.
Integers are whole numbers that can be positive, negative, or zero. For example, -3, 0, and 7 are all integers. On the other hand, rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. In simpler terms, a rational number can be written in the form of a/b, where a and b are integers and b ≠ 0.
Let’s illustrate this with a few examples:
- The integer 5 can be expressed as a rational number in multiple ways, such as 5/1 or 10/2.
- The integer -2 can also be represented as -2/1 or -4/2.
- Even zero is a rational number since it can be written as 0/1.
Since any integer can be represented as a fraction with a denominator of 1, it meets the criteria for being a rational number. Therefore, we can confidently conclude that all integers are rational numbers.
In summary, integers, by their very nature, fall within the broader category of rational numbers, illustrating the foundational concepts of number types in mathematics.