A rational number in a computer system is typically represented as a fraction, which consists of two integers: a numerator and a denominator.

To elaborate, a rational number is defined as a number that can be expressed as the quotient of two integers, with the condition that the denominator is not zero. In computer systems, these numbers are frequently represented as a pair of integers—specifically, the numerator and the denominator. This representation is commonly implemented using a data structure or a class that encapsulates these two integers and provides methods for performing various arithmetic operations on them.

For instance, in Python, you could represent a rational number using a simple class like the following:

'''python class Rational: def init(self, numerator, denominator): self.numerator = numerator self.denominator = denominator '''

In this ‘Rational’ class, the numerator and denominator are stored as instance variables. You could extend this class by adding methods to perform operations such as addition, subtraction, multiplication, and division.

Alternatively, rational numbers can be represented in a computer system using floating-point numbers. However, this approach may introduce precision errors, as not all rational numbers can be precisely represented in floating-point format. For example, the fraction $\frac{1}{3}$ cannot be exactly represented as a floating-point number, which results in small errors during calculations involving this number.

In contrast, representing rational numbers as pairs of integers can eliminate these precision errors, provided that the numerator and denominator do not exceed the integer type’s range. However, this method may incur slower performance and higher memory usage compared to floating-point representations, especially when dealing with large numbers or complex calculations.

In conclusion, the optimal method for representing rational numbers in a computer system largely depends on the specific requirements of the application, such as the need for precision, processing speed, or memory efficiency.