๐ Number System โ Complete Concept Guide
For School Students & Competitive Exams
1๏ธโฃ Introduction
The Number System is the foundation of mathematics. It helps us represent quantities and perform arithmetic operations.
Natural โ Whole โ Integers โ Rational โ Real
2๏ธโฃ Types of Numbers
๐น Natural Numbers (N)
1, 2, 3, 4, ... (Counting numbers)
๐น Whole Numbers (W)
0, 1, 2, 3, ...
๐น Integers (Z)
..., -3, -2, -1, 0, 1, 2, 3, ...
๐น Rational Numbers (Q)
Numbers that can be written as p/q (q โ 0)
๐น Irrational Numbers
โ2, ฯ, โ3 (Non-terminating, non-repeating decimals)
๐น Real Numbers (R)
All rational + irrational numbers
3๏ธโฃ Even, Odd, Prime & Composite
- Even: Divisible by 2 (2, 4, 6...)
- Odd: Not divisible by 2 (1, 3, 5...)
- Prime: Exactly 2 factors (2, 3, 5, 7...)
- Composite: More than 2 factors
4๏ธโฃ Place Value Concept
In 6,754 โ
- 7 is in the hundreds place โ 700
- 5 is in the tens place โ 50
- 4 is in the ones place โ 4
5๏ธโฃ Binary & Hexadecimal
| System | Base | Example |
|---|---|---|
| Binary | 2 | 10 = 1010 |
| Hexadecimal | 16 | 255 = FF |
6๏ธโฃ GCF & LCM
GCF: Greatest Common Factor
Example: GCF of 24 & 36 = 12
LCM: Least Common Multiple
Example: LCM of 6 & 8 = 24
7๏ธโฃ Exercise - 1
โ 234 + 567 = 801
โ 876 - 345 = 531
โ 12 ร 8 = 96
โ 42 รท 6 = 7
โ Binary of 10 = 1010
8๏ธโฃ Exercise - 2
โ 8 is Even
โ 9 is Odd
โ Factors of 24 โ 1,2,3,4,6,8,12,24
โ โ2 is Irrational
โ 3.7 ร 10โด is Scientific Notation
๐ฅ Final Revision Summary
โ Natural numbers start from 1
โ Whole numbers start from 0
โ 2 is the only even prime
โ Irrational numbers never repeat
โ All integers are rational
โ All rational numbers are real
