A rational number is defined as any number that can be expressed as the ratio of two integers, where the numerator is an integer and the denominator is a non-zero integer. In simpler terms, it can be written in the form p/q, with p and q being integers and q ≠ 0.
Rational numbers can be represented in different forms, including:
- Fraction: As mentioned, the most straightforward way to represent a rational number is through a fraction format, such as 1/2, 3/4, or -5/2.
- Decimal: Rational numbers can also be expressed as decimals. When converted from a fraction, they can result in either a terminating decimal (like 0.75 from 3/4) or a repeating decimal (like 0.333… from 1/3). Repeating decimals are characterized by a digit or group of digits that continue infinitely.
- Mixed Number: A rational number that is greater than one can be written as a mixed number, which consists of an integer and a proper fraction. For example, 2 1/2 represents the rational number 5/2.
Understanding rational numbers is crucial in mathematics, as they form the foundation for more complex number systems, and recognizing how they can be represented in different ways enhances our ability to work with them in various mathematical contexts.