1 CHAP

# 1 CHAP - 1 NUMBERS IMPORTANT FACTS AND FORMULAE I.Numeral...

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1. NUMBERS IMPORTANT FACTS AND FORMULAE I..Numeral : In Hindu Arabic system, we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 called digits to represent any number. A group of digits, denoting a number is called a numeral. We represent a number, say 689745132 as shown below : Ten Crores (10 8 ) Crore s(10 7 ) Ten Lacs (Millions ) (10 6 ) Lacs( 10 5 ) Ten Thous ands (10 4 ) Thous ands (10 3 ) Hundr eds (10 2 ) Ten s(1 0 1 ) Uni ts(1 0 0 ) 6 8 9 7 4 5 1 3 2 We read it as : 'Sixty-eight crores, ninety-seven lacs, forty-five thousand, one hundred and thirty-two'. II Place Value or Local Value of a Digit in a Numeral : In the above numeral : Place value of 2 is (2 x 1) = 2; Place value of 3 is (3 x 10) = 30; Place value of 1 is (1 x 100) = 100 and so on. Place value of 6 is 6 x 10 8 = 600000000 III.Face Value : The face value of a digit in a numeral is the value of the digit itself at whatever place it may be. In the above numeral, the face value of 2 is 2; the face value of 3 is 3 and so on. IV.TYPES OF NUMBERS 1.Natural Numbers : Counting numbers 1, 2, 3, 4, 5,. .... are called natural numbers. 2 . Whole Numbers : All counting numbers together with zero form the set of whole numbers . Thus, (i) 0 is the only whole number which is not a natural number. (ii) Every natural number is a whole number. 3 . Integers : All natural numbers, 0 and negatives of counting numbers i.e., {…, - 3 , - 2 , - 1 , 0, 1, 2, 3,…. .} together form the set of integers. (i) Positive Integers : {1, 2, 3, 4, …. .} is the set of all positive integers. (ii) Negative Integers : {- 1, - 2, - 3,…. .} is the set of all negative integers. (iii) Non-Positive and Non-Negative Integers : 0 is neither positive nor negative. So, {0, 1, 2, 3,….} represents the set of non-negative integers, while {0, - 1 , - 2 , - 3 , …. .} represents the set of non-positive integers. 4. Even Numbers : A number divisible by 2 is called an even number, e.g., 2, 4, 6, 8, 10, etc. 5. Odd Numbers : A number not divisible by 2 is called an odd number. e.g., 1, 3, 5, 7, 9, 11, etc. 6. Prime Numbers : A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself. Prime numbers upto 100 are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

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Prime numbers Greater than 100 : Letp be a given number greater than 100. To find out whether it is prime or not, we use the following method : Find a whole number nearly greater than the square root of p. Let k > *jp. Test whether p is divisible by any prime number less than k. If yes, then p is not prime. Otherwise, p is prime. e.g,,We have to find whether 191 is a prime number or not. Now, 14 > V191. Prime numbers less than 14 are 2, 3, 5, 7, 11, 13.
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1 CHAP - 1 NUMBERS IMPORTANT FACTS AND FORMULAE I.Numeral...

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