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What Is a Rational Number?

Modern mathematical theory classifies numbers and mathematical expressions as either rational or irrational numbers. This nomenclature is not based on whimsical notions of integers, but rather on straightforward mathematical theory.
  1. Rational Numbers

    • Rational numbers are defined as finite numbers. This can be a whole number, a decimal, a fraction, zero or a negative number. Even the value of π (pi), which is expressed as the number 3.1415926535897932384626433, is considered a rational number, because the above decimal is finite.

    Irrational Numbers

    • Irrational numbers defy finite mathematical description. A good example is the square root of two, which, when divided out longhand, has no end to its decimal notation.

    Fractions

    • Fractions are considered rational numbers, even for numbers like 1/3 and 2/3, which has a continuous decimal expression. It is the fact that each number can be expressed as a whole fraction that makes these numbers part of the rational subgroup.

    Square Roots

    • Square roots with evenly divided numbers are considered to be rational numbers. These square roots progress in this familiar sequencer, 1, 4, 9, 16, 25 and so forth. If looked at closely, you will see that each number has an even square root. They are (in sequence) 1, 2, 3, 4, 5 and so forth.

    Zero

    • Zero (0) is a rational number. Perhaps this is an arbitrary decision, but because zeros located midway between 1 and -1, it is considered a rational number


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