2 is a rational number because it can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. According to the reference provided, a number is rational if it can be written in the form p/q, where q ≠ 0.
Understanding Rational Numbers
Rational numbers are a fundamental concept in mathematics. They include all numbers that can be written as a ratio of two integers. Let's break down why 2 fits this description:
- Definition: A rational number is any number that can be expressed in the form of p/q, where:
- p is an integer (positive, negative, or zero)
- q is an integer, but q cannot be zero
Why 2 is Rational
The reference states that 2 is rational because it "can be written in p/q form which is mathematically represented as 2/1, where 1≠0".
- Example: The number 2 can be written as the fraction 2/1.
- Here, p = 2 (an integer)
- And q = 1 (an integer and not zero)
This fulfills the requirement that it can be expressed as a fraction of two integers, with the denominator not being zero, thus making it a rational number.
Examples of Rational Numbers
Here's a quick look at other examples of rational numbers:
- Integers: All integers are rational numbers (e.g., -3 can be written as -3/1, 0 as 0/1, 5 as 5/1)
- Fractions: Common fractions like 1/2, 3/4, or -7/8 are inherently rational.
- Terminating Decimals: Decimals that end, like 0.5 (which is 1/2) and 0.75 (which is 3/4), are also rational.
- Repeating Decimals: Decimals with a repeating pattern, such as 0.333... (1/3) and 0.142857142857... (1/7) are rational.
Why some numbers are NOT rational
The reference also gives examples of numbers that are not rational. Numbers like square roots ( √19 = 4.35889, √2 = 1.424 etc) are examples of irrational numbers. These numbers cannot be written as a simple fraction of two integers because their decimal representations are non-repeating and non-terminating.
Conclusion
In summary, 2 is a rational number because it can be precisely expressed as a fraction of two integers (2/1), where the denominator is not zero, as highlighted in the provided reference.
