What are rational numbers?

Rational numbers are defined as numbers that can be expressed as the quotient or ratio of two integers, where the denominator is not zero. This definition encompasses all integers, fractions, and some terminating or repeating decimals, as all of these can be represented in the form of a/b, where 'a' and 'b' are integers.

By understanding that rational numbers include fractions and ratios, it's clear how this definition supports the concept. For example, the number 3 can be expressed as 3/1, and the fraction 1/2 clearly highlights a ratio. This characteristic allows rational numbers to be distinguished from irrational numbers, which cannot be expressed in such a manner.

The other options do not accurately reflect the definition of rational numbers. While it is true that rational numbers can be written as decimals, not all decimals qualify as rational; non-terminating, non-repeating decimals are examples of irrational numbers and would not fit the definition. Additionally, rational numbers encompass both positive and negative numbers—not just negative ones. Lastly, the assertion that rational numbers cannot be expressed mathematically is fundamentally incorrect, as they are a well-defined subset of the number system and can be expressed through various mathematical forms.