Number System Notes : Classs 5th to 8th
1. Number Ending with 8 – Not a Perfect Square
If a number has 8 in the unit place, it can never be a perfect square.
Ex: 18, 28, 48, 78 → none are perfect squares.
āĻ¯āĻĻāĻŋ āĻā§āĻ¨ā§ āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻāĻāĻ āĻ¸ā§āĻĨāĻžāĻ¨āĻ¤ ā§Ž āĻĨāĻžāĻā§, āĻ¤ā§āĻ¨ā§āĻ¤ā§ āĻ¸ā§āĻāĻā§ āĻā§āĻ¤āĻŋāĻ¯āĻŧāĻžāĻ āĻĒā§ā§°ā§āĻŖ āĻŦā§°ā§āĻ āĻ¨āĻšāĻ¯āĻŧāĨ¤
āĻāĻĻāĻžāĻšā§°āĻŖ: ā§§ā§Ž, ā§¨ā§Ž, ā§Ēā§Ž, ā§ā§Ž → āĻāĻžāĻā§āĻ āĻĒā§ā§°ā§āĻŖ āĻŦā§°ā§āĻ āĻ¨āĻšāĻ¯āĻŧāĨ¤
2. First Odd Divisible Number (Nine – 9)
Nine (9) is the first odd number that is also a composite number (divisible by 1, 3, 9).
āĻ¨ā§ą (ā§¯) āĻšā§āĻā§ āĻĒā§ā§°āĻĨāĻŽ āĻŦāĻŋāĻā§āĻĄāĻŧ āĻ¸āĻāĻā§āĻ¯āĻž āĻ¯āĻŋ āĻ¯ā§āĻāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻžāĻ āĻŦā§āĻ˛āĻŋāĻŦ āĻĒāĻžā§°āĻŋ (ā§§, ā§Š, ā§¯-āĻ āĻŦāĻŋāĻāĻžāĻā§āĻ¯)āĨ¤
3. Natural Numbers (āĻ¸ā§āĻŦāĻžāĻāĻžā§ąāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž)
Numbers starting from 1 and used for counting are called natural numbers. Ex: 1, 2, 3, 4, …
ā§§ āĻĒā§°āĻž āĻā§°āĻŽā§āĻ āĻšā§ā§ąāĻž āĻāĻŖāĻ¨āĻžā§° āĻ¸āĻāĻā§āĻ¯āĻž āĻā§āĻāĻāĻž āĻ¸ā§āĻŦāĻžāĻāĻžā§ąāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻžāĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§§, ā§¨, ā§Š, ā§Ē…
4. Zero (āĻļā§āĻ¨ā§āĻ¯)
Zero means nothing. It has many unique mathematical properties.
āĻļā§āĻ¨ā§āĻ¯ā§° āĻ ā§°ā§āĻĨ “āĻāĻā§ āĻ¨āĻžāĻ’’āĨ¤ āĻāĻ¯āĻŧāĻžā§° āĻŦāĻšā§ āĻŦāĻŋāĻļā§āĻˇ āĻā§āĻŖ āĻāĻā§āĨ¤
5. Whole Numbers (āĻĒā§ā§°ā§āĻŖ āĻ¸āĻāĻā§āĻ¯āĻž)
Whole numbers = 0 + natural numbers. Ex: 0, 1, 2, 3, 4…
āĻļā§āĻ¨ā§āĻ¯ āĻā§°ā§ āĻ¸ā§āĻŦāĻžāĻāĻžā§ąāĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž āĻŽāĻŋāĻ˛āĻžāĻ āĻĒā§ā§°ā§āĻŖ āĻ¸āĻāĻā§āĻ¯āĻž āĻšāĻ¯āĻŧāĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§Ļ, ā§§, ā§¨, ā§Š…
6. Integers (āĻĒā§ā§°ā§āĻŖāĻžāĻā§āĻ)
Integers include:
negative numbers, zero, positive numbers
Ex: -3, -2, -1, 0, 1, 2, 3…
āĻĒā§ā§°ā§āĻŖāĻžāĻā§āĻāĻ¤ āĻĨāĻžāĻā§—
āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ āĻ¸āĻāĻā§āĻ¯āĻž, āĻļā§āĻ¨ā§āĻ¯, āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ āĻ¸āĻāĻā§āĻ¯āĻž āĻāĻĻāĻžāĻšā§°āĻŖ: -ā§Š, -ā§¨, -ā§§, ā§Ļ, ā§§, ā§¨, ā§Š…
7. Even Numbers (āĻ¯ā§āĻāĻšāĻž āĻ¸āĻāĻā§āĻ¯āĻž):
Numbers divisible by 2 without remainder. Ex: 2, 4, 6, 8, 10…
āĻ¯āĻŋāĻ¸āĻŦ āĻ¸āĻāĻā§āĻ¯āĻž ā§¨-āĻ āĻāĻžāĻ āĻĻāĻŋāĻ˛ā§ āĻ āĻŦāĻļāĻŋāĻˇā§āĻ āĻ¨āĻžāĻĨāĻžāĻā§āĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§¨, ā§Ē, ā§Ŧ, ā§Ž, ā§§ā§Ļ…
8. Odd Numbers (āĻŦāĻŋāĻā§āĻĄāĻŧ āĻ¸āĻāĻā§āĻ¯āĻž):
Numbers that leave remainder 1 when divided by 2. Ex: 1, 3, 5, 7…
āĻ¯āĻŋāĻ¸āĻŦ āĻ¸āĻāĻā§āĻ¯āĻž ā§¨-āĻ āĻāĻžāĻ āĻĻāĻŋāĻ˛ā§ ā§§ āĻ āĻŦāĻļāĻŋāĻˇā§āĻ āĻĨāĻžāĻā§āĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§§, ā§Š, ā§Ģ, ā§…
9. Prime Numbers (āĻŽā§āĻ˛āĻŋāĻ āĻ¸āĻāĻā§āĻ¯āĻž)
Numbers divisible only by 1 and itself. Ex: 2, 3, 5, 7, 11…
āĻ¯āĻŋāĻ¸āĻŦ āĻ¸āĻāĻā§āĻ¯āĻž āĻā§ā§ąāĻ˛ ā§§ āĻā§°ā§ āĻ¨āĻŋāĻā§ āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§¨, ā§Š, ā§Ģ, ā§, ā§§ā§§…
10. Composite Numbers (āĻ¯ā§āĻāĻŋāĻ ā¤¸ā¤ā¤āĨā¤¯ā¤ž)
Numbers divisible by more than two numbers. Ex: 4, 6, 8, 9, 10…
āĻ¯āĻŋāĻ¸āĻŦ āĻ¸āĻāĻā§āĻ¯āĻž āĻĻā§āĻāĻž āĻ¸āĻāĻā§āĻ¯āĻžā§° āĻ āĻ§āĻŋāĻāĻ¤ āĻŦāĻŋāĻāĻžāĻā§āĻ¯āĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§Ē, ā§Ŧ, ā§Ž, ā§¯, ā§§ā§Ļ…
11. Rational Numbers (āĻĒā§°āĻŋāĻŽā§āĻ¯āĻŧ āĻ¸āĻāĻā§āĻ¯āĻž)
Numbers that can be written as p/q, where p and q are integers and q ≠ 0. Ex: 4, –3, 22/7, √25 (=5)
āĻ¯āĻŋāĻ¸āĻŦ āĻ¸āĻāĻā§āĻ¯āĻž p/q ā§°ā§āĻĒā§ āĻ˛āĻŋāĻāĻŋāĻŦ āĻĒā§°āĻž āĻ¯āĻžāĻ¯āĻŧ āĻā§°ā§ q ≠ 0āĨ¤ āĻāĻĻāĻžāĻšā§°āĻŖ: ā§Ē, –ā§Š, ā§¨ā§¨/ā§, √ā§¨ā§Ģ (=ā§Ģ)