Is it true that every rational number is a whole number?

False. While it’s true that all whole numbers are rational numbers, not every rational number can be classified as a whole number. To understand this better, let’s clarify the definitions:

  • Rational Numbers: These are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. For example, &frac{1}{2}, 0, and 3 are all rational numbers.
  • Whole Numbers: This category includes all non-negative integers starting from 0. It encompasses numbers such as 0, 1, 2, 3, and so forth.

From this definition, it’s clear that while every whole number (like 3, 5, etc.) can be expressed as a rational number (for instance, 3 can be written as &frac{3}{1}), the reverse is not true. Rational numbers can include fractions and decimals, such as &frac{1}{2} or 2.5, which do not fit into the whole number category. Therefore, there are countless rational numbers that are not whole numbers.

In summary, while whole numbers are a subset of rational numbers, many rational numbers are not whole numbers, making the statement false.

Leave a Comment