A rational number (as studied in Class 9 math) is any number that can be expressed in the form p/q, where p and q are integers, and q is not equal to zero.
In simpler terms:
- p and q are integers: This means they can be positive or negative whole numbers, or zero (for p only). Examples: -3, 0, 5, -100.
- q ≠ 0: The denominator (q) cannot be zero. Division by zero is undefined.
- Form p/q: The number can be written as a fraction.
Examples of rational numbers:
- 1/2
- -3/4
- 5 (which can be written as 5/1)
- 0 (which can be written as 0/1)
- -7 (which can be written as -7/1)
- 0.25 (which can be written as 1/4)
- Repeating decimals like 0.333... (which is 1/3)
Examples of numbers that are NOT rational:
- √2 (square root of 2 - an irrational number)
- π (pi - an irrational number)
Key takeaways:
- Integers are rational numbers: Any integer 'n' can be written as n/1.
- Terminating decimals are rational numbers: A decimal that ends (like 0.75) can be expressed as a fraction (75/100).
- Repeating decimals are rational numbers: A decimal with a repeating pattern (like 0.333...) can be expressed as a fraction (1/3).
- Irrational numbers are NOT rational numbers: Numbers like √2 and π cannot be expressed as a fraction of two integers.
Rational numbers are a fundamental concept in Class 9 math, laying the groundwork for understanding real numbers and more advanced algebraic concepts.
