Yes, every integer is a rational number.
Understanding Integers and Rational Numbers
To understand why every integer is a rational number, let's define these terms:
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Integers: As the reference states, integers consist of zero, natural numbers (1, 2, 3...), and the additive inverses of those numbers (-1, -2, -3...). Examples of integers include -3, -2, -1, 0, 1, 2, and 3.
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Rational Numbers: A rational number is any number that can be expressed as a fraction p/q, where p and q are integers, and q is not equal to zero.
Why Integers are Rational Numbers
Any integer n can be written as the fraction n/1. Since n is an integer and 1 is also an integer, and 1 is not zero, n/1 fits the definition of a rational number.
Examples:
- 5 can be written as 5/1.
- -3 can be written as -3/1.
- 0 can be written as 0/1.
Therefore, because every integer n can be expressed in the form n/1, where both n and 1 are integers and 1 ≠ 0, every integer satisfies the definition of a rational number. The assertion "Every integer is a rational number" is TRUE.
