Which type of numbers cannot be expressed as a ratio of two integers?

Irrational numbers are those that cannot be represented as a ratio of two integers. They have non-repeating, non-terminating decimal expansions, which means that they cannot be exactly expressed as a fraction a/b, where both a and b are integers and b is not zero. Examples of irrational numbers include the square root of 2, pi, and the number e.

In contrast, rational numbers are defined as numbers that can be expressed as the ratio of two integers, which includes integers and fractions. Since integers are whole numbers, they also fall under the category of rational numbers because any integer can be expressed as a ratio by using 1 as the denominator (for example, the integer 3 can be expressed as 3/1). Prime numbers, being a subset of integers greater than 1 that have no divisors other than 1 and themselves, can also be expressed as ratios. Thus, the defining characteristic of irrational numbers is what separates them from these other types of numbers.