A rational number is defined as any number that can be expressed as the ratio of two integers, where the numerator is an integer and the denominator is a non-zero integer. This can be represented in the mathematical form of p/q, where p and q are integers and q ≠ 0.
For example, the number 3 can be represented as the ratio 3/1 since both 3 and 1 are integers. Similarly, the number -4 can be expressed as -4/1 or -8/2. In both cases, we adhere to the rule that the denominator cannot be zero.
Rational numbers can also be represented as decimals. If the decimal representation terminates (like 0.75), it can still be expressed as a ratio; in this case, 0.75 can be written as 75/100, which simplifies to 3/4.
Additionally, repeating decimals, such as 0.333…, can also be converted into rational numbers. This decimal can be expressed as the ratio 1/3, illustrating once again the fundamental principle of rational numbers being the ratio of two integers.
In summary, any rational number can effectively be expressed as a fraction p/q as long as the denominator is not zero, showcasing the versatility and inherent structure of rational numbers within the broader set of real numbers.