A rational number is any number that can be expressed as the ratio or fraction of two integers, where the denominator is not zero. In mathematical terms, a rational number is a number of the form:

$\frac{a}{b}$

where:

• $a$ and $b$ are integers (i.e., whole numbers or negative whole numbers), and
• $b \neq 0$ (because division by zero is undefined).

Examples of Rational Numbers:

• $\frac{3}{4}$ (Here, 3 is the numerator and 4 is the denominator)
• $\frac{-7}{2}$ (A negative rational number)
• $5$ (This can be written as $\frac{5}{1}$, so it's rational)
• $0$ (This can be written as $\frac{0}{1}$)

Properties of Rational Numbers:

1. Closure under addition, subtraction, multiplication, and division: If you add, subtract, multiply, or divide two rational numbers (where the division doesn't involve dividing by zero), the result will always be a rational number.
2. Decimal representation: The decimal form of a rational number either terminates (like 0.75 or 0.25) or repeats (like 0.333... or 1.666...).
3. Countability: Rational numbers are countable, meaning they can be listed in a sequence, even though there are infinitely many of them.

Would you like to explore more details or have specific examples you'd like to go over?

Related Questions:

1. What is the difference between a rational and an irrational number?
2. How do you convert a repeating decimal into a fraction?
3. Can all fractions be considered rational numbers?
4. What is the relationship between rational numbers and real numbers?
5. What are some common applications of rational numbers in real life?

Tip: Any integer is a rational number because it can always be expressed as a fraction with a denominator of 1 (e.g., $5 = \frac{5}{1}$).