Final Answer:
Rational numbers are numbers that can be written as fractions or quotients of integers. Rational numbers include integers, decimals, and fractions such as 1/2 or 0.75. Irrational numbers, on the other hand, cannot be expressed as fractions. They include square roots of non-perfect squares, such as √2 or √5.
Step-by-step explanation:
Rational numbers are those that can be expressed as the ratio of two integers, i.e., in the form p/q, where p and q are integers and q is not equal to zero. This includes integers (whole numbers), decimals, and fractions. For example, the number 3 can be written as 3/1, making it a rational number. Similarly, 0.6 is a rational number as it can be expressed as 6/10, and so on.
On the other hand, irrational numbers cannot be represented as fractions. They have non-repeating, non-terminating decimal expansions. A classic example is the square root of non-perfect squares, like √2 or √5. These numbers cannot be expressed as a simple fraction of two integers. For instance, √2 is approximately 1.414, and its decimal expansion goes on infinitely without repeating.
In summary, rational numbers encompass a broad range of numerical forms that can be expressed as fractions or ratios of integers, while irrational numbers include those with non-repeating, non-terminating decimal expansions, particularly the square roots of non-perfect squares.