Rational aur Irrational Numbers
Rational Numbers (Aqalmand Numbers 😂)
Ye wo numbers hain jo fraction (p/q) ki form mein likhe ja
sakte hain.
Matlab, do numbers ka ratio hota hai jise hum divide kar sakte
hain.
✅ Examples:
- 5 → Isko hum 5/1
likh sakte hain, yani ye fraction hai.
- 1/2 → Ye to waise hi fraction hai.
- 0.75 → Isko 3/4
likh sakte hain, yani ye bhi rational hai.
- 1.3333... (Repeating Decimal) → Isko 4/3 likh sakte hain, yani ye bhi rational hai.
💡 Aasan Rule:
- Jo
number fraction (p/q) ki form mein likha ja sake,
wo rational hota hai.
- Agar decimal khatam ho jaye ya repeat kare, to
wo rational hota hai.
Irrational Numbers (Bewaquf Numbers 😂)
Ye wo numbers hain jo fraction (p/q) ki form mein nahi likhe ja
sakte.
Matlab, inka decimal kabhi khatam nahi hota aur repeat bhi nahi karta.
❌ Examples:
- π (pi) = 3.1415926535... (Ye kabhi end nahi
hota aur repeat bhi nahi karta).
- √2 = 1.414213562... (Iska bhi decimal end nahi
hota).
- √3, √5, √7 (Jo square root perfect square nahi hai, wo irrational hoga).
💡 Aasan Rule:
- Agar decimal non-terminating (khatam na ho) aur non-repeating
(repeat na kare) ho, to wo irrational hai.
- Agar ek number fraction ki form mein nahi likha ja sakta, to
wo irrational hai.
Ek Simple Table for Quick Understanding
|
Feature |
Rational Numbers |
Irrational Numbers |
|
Fraction Form (p/q)? |
Haan (5 = 5/1, 0.5 = 1/2) |
Nahi (Ï€, √2, √3) |
|
Decimal Ending? |
Haan (0.75, 1.5) |
Nahi (3.141592..., 1.414213...) |
|
Decimal Repeating? |
Haan (0.333..., 1.666...) |
Nahi (0.1010010001...) |
|
Example Numbers |
3, 5/2, 0.4,
-7, 1.25 |
Ï€, √2, √3, √7 |
😃