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Class – VI 1 NUMBER SYSTEM Natural numbersCounting numbers started by 1 are called “Natural numbers” The set of natural numbers is denoted as N = { 1, 2, 3, ……………} 2 Whole NumbersNatural numbers including “0” (zero) are called whole numbers The set of whole numbers is W = { 0, 1, 2, 3 ……….} 3 IntegersWhole numbers including natural numbers with negative sign are called “Integers” The set of integers is I or Z = { ………-3, -2, -1, 0, 1, 2, 3 …………} (a) Odd numbers – 1, 3, 5, 7, ………… (b) Even numbers- 0, 2, 4, 6, ………… (c) Prime number- Number divisible by one and itself only 2, 3, 5, 7, 11, 13, 17….. 4 Rational NumbersNumber of the form p/q where p, q I and q 0 are called rational numbers. p Q , p & q are integers & q 0 q Decimal form of rational numbers (i) The number of digits are finite after decimal (Terminating decimal) For example – (a) -0.5 (b) 3.654 (ii) 5 The number of digits are infinite after decimal and repetition of the digits are there (non-terminating, recurring decimal) For example – (a) 1.525252.......... .... 1.52 (b) 2.148148148........ 2.148 Irrational numbersNumbers which are non-terminating, non-recurring are called irrational numbers. Example- 2, 3, 7 The most popular irrational numbers (i) 3.1459265.......... ...... (ii) e 2.7182818.......... ....... ________________________________________________________________________________________ Address : 61, First Floor, Chanakya Plaza, New CG Road, Chandkheda, Ahmedabad Contact : 96017 55017 , 90999 66717 www.abhigyanam.com Some results on irrational numbers: 1 Negative of an irrational number is an irrational number. 2 SUM, DIFFERENCE, PRODUCT & QUOTIENT of a rational and an irrational number is an irrational number. 3 SUM, DIFFERENCE, PRODUCT & QUOTIENT of two irrational numbers may be rational or an irrational number. 6 Real numbersNumbers including rational and irrational numbers are called “real numbers” Representation of real numbers on numbers line. -4 -3 -2 -1 0 1 2 3 4 5 Each and every point on the line represents a definite real number Each and every real number has definite chair on number line. All real numbers can be represented on a number line. FOR MORE CHAPTER NOTES MAIL YOUR EMAIL- ID ON [email protected] m OR Direct get in pdf form whatsapp on 9099966717 ________________________________________________________________________________________ Address : 61, First Floor, Chanakya Plaza, New CG Road, Chandkheda, Ahmedabad Contact : 96017 55017 , 90999 66717 www.abhigyanam.com