The set of numbers that are real numbers but cannot be expressed as one integer divided by another are called irrational numbers.
Rational numbers are those that can be expressed as a fraction of two integers (where the denominator is not zero), which is the definition of numbers that can be expressed as one integer divided by another.
Examples of irrational numbers include \(\sqrt{2}\), \(\pi\), and \(e\). These numbers cannot be precisely expressed as a fraction of two integers.
In summary, the correct answer is irrational.