PRESENTATION BY DIVYAM kumar -1.pptx mathematics
- 1. PRESENTATION BY DIVYAM KUMAR CLASS- 9th B NUMBER SYSTEM
- 2. CONTEXT Presentation title • TYPES OF NUMBER SYSTEM • RELATED RULES • QUESTIONS/EXAMPLES • SUMMARY • HISTORY OF THE TOPIC • INTRODUCTON NUMBER SYSTEM
- 3. HISTORY OF NUMBER SYSTEM The history of number system dates back thousands of years ,with a early civilization like ancient Babylonians ,Sumerians etc. developing their own system. The HinduArabic number system introduced in the 7th century AE revolutionized mathematics with followed use of digits
- 4. 4 INTRODUCTION A NUMBER SYSTEM IS OF WRITING FOR EXPRESSING NUMBERS . IT IS THE MATHEMATICAL NOTATION FOR REPRESENTING NUMBERS OF A GIVEN SET BY USING DIGITS OR OTHER SYMBOLS IN A CONSTANT MANNER . IT PROVIDES A UNIQE REPRESENTATION TO EVERY NUMBER AND REPRESENT THE ARTHEMATICS AND AIGEBRAIC STRUCTURE OF THE FIGURES . IT ALSO ALLOWS US TO OPERATE ARTHEMATICS OPERATIONS LIKE ADDATION , SUBTRATION AND DIVISION
- 5. TYPES OF NUMBER SYSTEM NUMBER SYSTEM DECIMAL NUMBERS BINARY NUMBERS OCTAL NUMBERS HEXADECIMAL NUMBERS BASE 10 (0,9) BASE 2 (0,1) BASE 16 (0,9,A..F) BASE 8 (0,7)
- 6. REAL NUMBER • NATURAL NUMBER :- COUNTING NUMBERS are KNOWN AS NATURAL NUMBER EG : THUS ,1,2,3,4,5,6 …etc. ., are ALL NATURAL NUMBER • WHOLE NUMBER :- ALL NATURAL NUMBERS TOGATHER WITH 0 FORM THE COLLECTION OF ALL WHOLE NUMBERS e.g. : 0,1,2,3,4,5,6,7 etc. • INTEGERS :- ALL NATURAL NUMBERS , 0 AND NEGATIVE OF NATURAL NUMBERS FORM THE COLLECTION OF ALL INTEGERS. EG. : THUS .. -5,-4,-3,-2,-1, 0,1,2,3,4 etc.. ARE ALL INTEGERS
- 7. RATIONAL NUMBER THE NUMBER IN THE FORM OF P/Q ,WHERE P & Q ARE INTEGERS AND Q !=0, ARE KNOWN AS RATIONAL NUMBERS. REMARKS :- (i) 0 IS A RATIONAL NUMBER, SINCE WE CAN WRITE ,0 =0/1. (ii) EVERY NATURAL NUMBER IS RATIONAL NUMBER , SINCE WE CAN WRITE , 1=1/1,2=2/1 etc.… (iii) EVERY INTEGER IS A RATIONAL NUMBER , SINCE AN INTEGER IS A RATIONAL NUMBER , SINCE AN INTEGER CAN BE WRITEN AS a/1.
- 8. PROPERTIES OF RATIONAL NUMBER RATIONAL NUMBERS FOLLOW THE COMMUTATIVE AND ASSOCIATIVE LAW OF ADDITION AND MULTIPLICATION.THEY ALSO FOLLOW THE DISTRIBUTIVE LAW OF MULTIPLICATION OVER ADDITION.IF A,B AND C ARE THRE NUMBERS , THEN a+b=b+a (commutative law of addition) A*b=b*a (commutative law of multiplication) A+(b+c)=(a+b)+c (associative law of addition) A*(b*c)=(a*b)*c (associative law of multiplication) A*(b+c)=a*b+a*c (law of distribution) (b+c)a=b*a+c*a (law of distribution)
- 9. 9 IRRATIONAL NUMBER A NUMBER WHICH CAN NEITHER BE EXPRESSED AS TERMINATING DECIMAL NOR AS A REPEATING DECIMAL, IS CALEED AN IRRATIONAL NUMBER. THUS , NON TERMINATING , NOIN REPEATING DECIMALS ARE IRRATIONAL NUMBERS.
- 10. PROPERTIES OF IRRATIONAL NUMBER (i) IRRATIONAL NUMBERS SATISFY THE COMMUTATIVE , ASSOCIATIVE AND DISTRIBUTIVE LAWS FOR ADDITION AND MULTIPLICATION. (ii) (a)SUM OF RATIONAL AND IRRATIONAL IS IRRATIONAL. (b)DIFFERENCE OF A RATIONAL AND AN IRRATIONAL IS IRRATIONAL. (c)PRODUCT OF RATIONAL AND AN IRRATIONAL IS IRRATIONAL. (d) QUOTINET OF A RATIONAL AND IRRATIONAL IS IRRATIONAL
- 11. Summary 11 Presentation title IN THIS CHAPTER I HAVE LEARNT MANY THINGS SOME OF THEM ARE • THE COCEPT OF REAL NUMER AND HISTORY OF NUMBER SYSTEM •MATHEMATICATION NAME OR HER CONTRIBUTION IN MATHEMATICS LIKE PYTHAGORAS ,HIPPACUS, ARCHYTAS • REPRESENTATION OF IRRATIONAL NUMBER IN THE NUMBER LINE • LAWS OF EXPONENTS FOR A REAL NUMBER • RATIONALISATION FACTORS or ETC…..
- 12. Thank you