0Rational Numbers?
In simple English, "rational" means something that is logical or makes sense. In mathematics, rational numbers are related to the concept of fractions. Let's travel back and review the lesson on fractions, specifically proper and improper fractions.
Proper fractions are fractions where the numerator (the top number) is smaller than the denominator (the bottom number). For example, 3/4
is a proper fraction.
Improper fractions are fractions where the numerator is larger than or equal to the denominator. For example, 5/3
is an improper fraction.
Both proper and improper fractions are members of the rational number family. Rational numbers are numbers that can be expressed in the form a/b
, where
𝑎 and 𝑏 are integers, and 𝑏 is not zero.
Now, what happens if the denominator becomes zero? What kind of fraction is that? Is it making any sense? No, it doesn't. Dividing by zero is undefined and does not produce a valid number. Therefore, rational numbers must have a denominator that is not zero. When you divide rational numbers, you get definite decimal places that either terminate or repeat.
In summary, rational numbers are fractions where the denominator is never zero, and their decimal expansions are predictable—they either end or follow a repeating pattern.
