Final answer:
Rational numbers can be expressed as a fraction and have a terminating or repeating decimal, while irrational numbers cannot be expressed as a fraction and have a non-repeating and non-terminating decimal. Comparing these types of numbers helps us understand their properties and relationships and has practical applications in solving problems involving measurements and estimations.
Step-by-step explanation:
Rational numbers are numbers that can be expressed as a fraction, while irrational numbers are numbers that cannot be expressed as a fraction and have an infinite number of non-repeating decimal digits. One way to compare rational and irrational numbers is by considering their decimal representations. Rational numbers will have a terminating or repeating decimal, while irrational numbers will have a non-terminating and non-repeating decimal.
We might want to compare these types of numbers to understand their properties, relationships, and applications. Comparing rational and irrational numbers can help us understand number systems, make estimations, solve real-world problems involving measurements, and comprehend mathematical principles and concepts.