Which statement describes the difference between rational and irrational numbers?

The statement that rational numbers can be written as fractions while irrational numbers cannot captures the fundamental distinction between these two types of numbers. Rational numbers are defined as numbers that can be expressed in the form of a fraction or ratio, where both the numerator and denominator are integers, and the denominator is not zero. Examples of rational numbers include 1/2, 3, and -4. On the other hand, irrational numbers cannot be expressed as simple fractions; they are numbers that have non-repeating, non-terminating decimal expansions, such as π (pi) and the square root of 2.

Understanding this difference is crucial, as it lays the foundation for concepts in number theory and helps in identifying and classifying numbers based on their properties. The other choices present inaccuracies about the characteristics of rational and irrational numbers, such as incorrect associations with integers, decimal behavior, or restrictions on positivity, which do not represent the true nature of these sets of numbers.