What is the relationship between a rational number and an irrational number?

The relationship between rational and irrational numbers is fundamentally rooted in their definitions and characteristics. Rational numbers are those which can be expressed as a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. This means they can include integers, whole numbers, terminating decimals, and repeating decimals.

On the other hand, irrational numbers cannot be expressed as a fraction. They are characterized by their non-repeating and non-terminating decimal expansions. This distinguishes them clearly from rational numbers. For example, the square root of 2 and pi (π) are both irrational, as they cannot be displayed as a simple ratio of integers and their decimal representations go on infinitely without repeating.

Thus, the correct answer identifies that while rational numbers can have decimal forms that are either repeating or terminating, irrational numbers are characterized specifically by their non-repeating decimal form, highlighting a key difference in their nature. This understanding is crucial when distinguishing between these two categories of numbers in mathematics.