Overview:
Rational numbers are numbers that can be expressed as a ratio of integers, such as 5/6, 12/3, or 11/6. The denominator can be 1, as in the case of every whole number, but the denominator cannot equal 0. Decimals must be able to be converted evenly into fractions in order to be rational.
Why Are Whole Numbers Rational?
Whole numbers are rational because they can be expressed as a ratio of integers such as 5/1, 10/1, 21/1, and so on. Although they are not usually written that way, it is sometimes useful to think of them that way, especially when using them in multiplication or division problems. For example, when solving a problem such as 1/6 of 12, it is easier to multiply 1/6 ∙ 12/1 = 12/6 = 2.
Which Decimals Are Rational Numbers?
Not all decimals are rational numbers, but only those that can be converted evenly into fractions (or ratios) are rational. Any decimal that terminates is rational, such as 0.25 (1/4), 0.125 (1/8), 0.625 (5/8). Also, decimals that repeat in a pattern are rational numbers, because they can also be converted evenly into fractions, such as 0.3333… (1/3), 0.1111 … (1/9), or 0.4166… (5/12).
How Many Numbers Are Rational?
There is an infinite set of rational numbers along the number line. In addition, the set of rational numbers is infinitely dense, which means that between any two rational numbers, another rational number can always be found.
Are There Numbers that Are Not Rational?
There is also a set of numbers that are not rational, because they cannot be expressed exactly with a fraction. Decimals that do not repeat, such as pi( π), are irrational, as well as square roots that are not exact, such as the square root of 2, 3, or 5. These irrational numbers, along with the set of rational numbers, compose the set of real numbers.
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