Rational Numbers:
A rational number is any number that can be written as a fraction (i.e., in the form p/q, where p and q are integers and q ≠ 0).
Examples:
1/2, -3/4, 5 (because 5 = 5/1), 0.75 (because 0.75 = 3/4), -2
Key Features:
Can be positive or negative
Includes integers, fractions, and terminating or repeating decimals
The decimal expansion either terminates (e.g., 0.5) or repeats (e.g., 0.333...)
Irrational Numbers:
An irrational number is a number that cannot be written as a fraction of two integers.
Examples:
√2, √3, π (pi), e, 0.101001000100001… (non-repeating, non-terminating decimal)
Key Features:
The decimal expansion does not terminate and does not repeat
Cannot be expressed exactly as a fraction
Commonly occur in geometry (like √2 from the diagonal of a square
Summary:
Let me know if you need this in Urdu or with a diagram.
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