NUMBER SYSTEM (संख्या पद्धति)|Classification of Numbers|YRS4learning Hi Students, In this video, I have explained the types of numbers we have in our #numbersystem.  Natural numbers  Whole numbers  Integers  Even numbers  Odd numbers  Prime numbers  Composite numbers  Co-prime numbers  Rational numbers  Irrational numbers  Real numbers  Imaginary numbers You can also watch my videos for the follwing topics:- Exercise 1.1 (Q. 1 (i) (ii)) Rational Numbers Chapter 1|Class 8 Maths | NCERT| CBSE https://youtu.be/zUttADoiANw Rational Numbers Chapter 1 |NCERT Class 8th Math https://youtu.be/Y6AEXvw-mcE Algebraic Identities For Class 8th & 9th | Part 2 | Identities class VIII & IX | YRS4learning https://youtu.be/gP1Rm5UG_JI Algebraic Identities For Class 8th & 9th | Part 2 | Identities class VIII & IX | YRS4learning https://youtu.be/gP1Rm5UG_JI Basic Concepts of Number System (संख्या पद्धति)|Classification of Numbers| YRS4learning https://youtu.be/YAjaiEcmnzE Coordinate geometry class 10|Coordinate Geometry | Class 10 Chapter 7 | https://youtu.be/JQoa1cltWRQ Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 | YRS4Learning https://youtu.be/Z_au2kZl0JI How to download NCERT Books 1st to 12th Class Free Download from Google |NCERT| YRS4learning https://youtu.be/n6-hZ3tYMh0

1. Key facts about NUMBER SYSTEM.
NUMBER SYSTEM | संख्या पद्धति |
संख्या पद्धति में याद
करने योग्य प्रमुख बािें|
Number Systems
BY :- SUKHWINDER KUMAR
For All Boards & Competitive Exams

2. NUMBER
DIGIT NUMERALS
BUILDING BLOCKS
Number Systems

3. How this IDEA is represented..
Number is an IDEA..
6
NUMBER
A NUMBER is a mathematical object
used to count, measure, and label.
(संख्या एक गणििीय वस्िु है जिसका उपयोग
गिना, माप और लेबल क
े ललए ककया िािा
है।)
e.g. 1,2,3,4….so far.

4. Conclusion: A number is an idea and the numeral is how we write it.
DIGIT
NUMERALS
Number Systems
DIGIT is a single
symbol used
alone or in
combinations to
make Numerals.
e.g. 0, 1, 2, 3, 4, 5,
6, 7, 8, 9
Numerals: A group of digits or signs or symbols or
name that stands for a number are called Numerals.
(संख्यांक:- संख्या को तनर्देलिि करने वाले अंकों अथवा संक
े िों
क
े समूह को संख्यांक कहा
िािा है|) e.g. 3, 49 and twelve are all numerals.
Let me explain, 3 is single digit but also a numeral.
Similarly, 49 is also a numeral but with two digits i.e.
4 & 9.
Also, forty nine is a numeral as it is name for 49.

5. NATURAL NUMBERS
1
TYPES OF NUMBERS
WHOLE NUMBERS
2
INTEGERS
3
EVEN NUMBERS
4
ODD NUMBERS
5
PRIME NUMBERS
6
प्राकृ ि संख्याएँ
Number Systems
पूर्ण संख्याएँ
पूर्ाांक संख्याएँ
सम संख्याएँ
विषम संख्याएँ
अभाज्य संख्याएँ

6. COMPOSITE NUMBERS
7
CO-PRIME NUMBERS
8
RATIONAL NUMBERS
9
IRRATIONAL NUMBERS
10
REAL NUMBERS
11
IMAGINARY NUMBERS
12
Number Systems
िास्िविक संख्याएँ
काल्पतनक संख्याएँ
अपररमेय संख्याएँ
पररमेय संख्याएँ
सह-अभाज्य संख्याएँ
भाज्य संख्याएँ
TYPES OF NUMBERS

7. NATURAL NUMBERS
1
Number Systems
प्राकृ ि संख्याएँ
All counting numbers are called Natural Numbers denoted by N.
E.g. 1, 2, 3, 4, 5, 6, 7 ,. . . . ∞ (to infinity).
Note:-
 Natural numbers are always positive ( धनात्मक ).
 1 is the smallest ( सबसे छोटी ) natural number.
 0 “Zero” is not a natural number.
वे संख्याएँ, जिनसे वस्िुओ की गिना की िािी है, प्राकृ ि संख्या
Or वस्िुओं को गगनने क
े ललए जिन संख्याओं का प्रयोग ककया िािा है, उन्हें गर्न संख्याएँ या प्राकृ ि संख्याएँ कहिे हैं|
Or गगनिी की प्रकिया को, प्राकृ ि संख्या कहा िािा है|
िैसे ;- 1, 2, 3, 4, 5, 6, 7, . . . . ∞ (अनंि िक).

8. WHOLE NUMBERS
2
Number Systems
पूर्ण संख्याएँ
All counting numbers including zero are called Whole Numbers denoted by W.
E.g. 0, 1, 2, 3, 4, 5, 6, 7 ,. . . . ∞ (to infinity).
Note:-
 Every natural number is whole number.
 0 is the smallest ( सबसे छोटी ) whole number.
 0 “Zero” is the starting number in whole numbers.
यदर्द प्राकृ ि संख्याओ में िून्य (0) को सजममललि कर ललया िाए, िो वे संख्याएँ पूर्ण संख्याएँ कहलािी हैं|
Or प्राकृ ि संख्या क
े समूह में िून्य को सजममललि करने पर िो संख्याएँ प्राप्ि होिी हैं, वे ‘पूिण संख्याएँ’ कहलािी हैं|
िैसे- 0, 1, 2, 3, 4, 5, 6, 7, . . . ∞

9. INTEGERS
3
Number Systems
पूर्ाणक संख्याएं
All counting numbers including zero and negatives of the counting numbers are called Integers
denoted by I.
E.g. -∞…….., -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7 ,. . . . ∞ (to infinity).
Note:-
 Integers are both positive and negative.
 Zero (0) is neither a positive nor negative integer number.
 I+ and I- are denoted as positive and negative integers ( धनात्मक और ऋिात्मक पूिाांक संख्या)
पूिण संख्याओ में ऋिात्मक संख्याओं को सजममललि करने पर िो संख्याएँ प्राप्ि होिी है वे संख्याएँ पूर्ाणक
संख्याएँ कहलािी हैं|
Or प्राकृ ि संख्याओं क
े समूह में िून्य एवं ऋिात्मक संख्याओं को सालमल करने पर िो संख्याएँ प्राप्ि होिी हैं, वे
संख्याएँ पूर्ाांक संख्या कहलािी हैं.
िैसे- -3, -2, -1, 0, 1, 2, 3, . . .

10. EVEN NUMBERS
4
Number Systems
सम संख्याएँ
Numbers which are completely divided by 2 are called Even Numbers.
E.g. 2, 4, 6, 8, 10, 12….so on.
वे संख्याएँ िो 2 से पूिणिः ववभाजिि हो िािी हैं उन्हें ‘सम संख्याएँ’ कहिे हैं|
िैसे 2, 4, 6, 8, 10, 12….so on.

11. ODD NUMBERS
5
Number Systems
विषम संख्याएँ
Numbers which are not completely divided by 2 are called Odd Numbers.
E.g. 1, 3, 5, 11, 17, 29, 39 ….so on.
वे संख्याएँ िो 2 से पूिणिः ववभाजिि नह ं होिी है, उन्हें ‘विषम संख्याएँ’ कहिे हैं|
िैसे 1, 3, 5, 11, 17, 29, 39 ….so on.

12. PRIME NUMBERS
6
Number Systems
अभाज्य संख्याएँ
Natural numbers having only two factors i.e. 1 and itself.
Or Those numbers which are not divisible by any number other than themselves and 1,
are called Prime Numbers.
E.g. 2, 3, 7, 11, 13, 17, 19…. So on.
वे संख्याएँ िो स्वयं और 1 क
े अलावा अन्य ककसी संख्या से ववभक्ि नह ं होिी हैं उन्हें ‘अभाज्य संख्याएँ’ कहिे हैं।
Let me explain with an example, suppose we have 13 and we look for its factor we found
that it has only two factors.
Factors of 13 are 1 & 13 itself.
Note: -
 1 is neither a Prime Number nor a Composite Number.
 There are twenty five (25) prime numbers between 0 to 100.

13. COMPOSITE NUMBERS
7
Number Systems
भाज्य संख्याएँ
Those numbers which are completely divisible by any number other than themselves and 1,
are called Composite Numbers.
E.g. 4, 6, 8, 9, 10, 12, 14, 15, ……so on.
वे संख्याएँ िो स्वयं और 1 क
े अतिररक्ि ककसी अन्य संख्या से पूिणिः ववभाजिि होिी है, िो
वह भाज्य संख्या कहलािी है|
Let me explain with an example, suppose we have 9 and we found that it has three factors
i.e. 1, 9, 3.
9 = 1 X 9, 3 X 3
Note: -The composite number is both even and odd.

14. CO-PRIME NUMBERS
8
Number Systems
सह-अभाज्य संख्याएँ
When there is no common factor except 1 in a group of two or more numbers, or whose HCF
(Highest Common Factor) = 1, they are called Co-Prime Numbers.
Or
Pairs (pairs) of numbers that do not have any common factors other than 1 in their factors
are called co-prime numbers.
Like- (4, 9), (12, 25), (8, 9, 13) etc.
िब र्दो या र्दो से अगधक संख्याओं में कोई भी उभयतनष्ठ गुिनखंड न हो अथवा जिसका म.स. 1 हो ,वे एक साथ ‘सह-
अभाज्य संख्याएँ’ कहलािी हैं।

15. RATIONAL NUMBERS
9
Number Systems
पररमेय संख्याएँ
Denoted by “Q” are numbers which can be written in p/q form, where p and q are integers and
q≠ 0.
वह संख्या िो p/q क
े रूप में ललखा िा सकिा है, उसे पररमेय संख्या कहिे है , िहाँ p िथा q पूिाांक हैं एवं
q ≠ 0 अथाणि p और q र्दोनों पूिाांक हो लेककन q कभी िून्य न हो.
िैसे- 4, 1.77 , 0 , 2/3 आदर्द|

16. Number Systems
RATIONAL NUMBERS
9
पररमेय संख्याएँ

17. IRRATIONAL NUMBERS
10
Number Systems
अपररमेय संख्याएँ
A number that cannot be written as p / q is called an irrational number.
Where p and q are integers and q ≠ 0
Like - √2, 5 + √3, √2, 5 1/3, π… ..
Note: -π is an irrational number.
वह संख्या जिसे p/q क
े रूप में नह ं ललखा िा सकिा है, वह अपररमेय संख्या कहलािी है.
िहाँ p िथा q पूिाांक हैं एवं q ≠ 0
िैसे – √2, 5 + √3 , √2 , 5 1/3 , π …..

18. NATURAL NUMBERS
Number Systems
IRRATIONAL NUMBERS
10
अपररमेय संख्याएँ

19. REAL NUMBERS
11
Number Systems
िास्िविक संख्याएँ
Real numbers include all rational and all irrational numbers. Denoted by “R”
e.g. 4 , 6, 2 ,√7, +4 , -2 etc.
Note:- The actual number is denoted by Rez or R.
सभी पररमेय िथा अपररमेय संख्याएँ ‘िास्िविक संख्याएँ’ कहलािी हैं।

20. IMAGINARY NUMBERS
12
Number Systems
काल्पतनक संख्याएँ
These numbers are complex numbers which can be written as real number multiplied by an imaginary
unit “i”called Imaginary Numbers.
Square root of a negative number where it doesnot have definite value.
Such as: −2 and −5 etc.
Note: -
 The imaginary number is denoted by Imz.
 The imaginary number when squared results in negative number.
ऋिात्मक संख्यायों का वगणमूल लेने पर िो संख्याएं बनिी हैं , उन्हें काल्पतनक संख्याएं कहिे हैं ।

21. With all this, we have covered all the
information related to
Classification of Number
System (definitions) and now
we won’t face any problem with the exercise.
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