NUMBERS – IMPORTANT FACTS

NUMBERS: We use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9 are called Digits, to represent any Number.

A Group of figures representing a number is called a Numeral.

Representation of a number in figures is called notation and expressing a number in words is called numeration.

Place value or Local value of a Digit in a Numeral:

Example: 657891232, in this Place value of 2 is (2X1) = 2; Place value of 3 is (3X10) = 30; Place value of 2 is (2X100) = 200; and so on.. then the place value of 6 is (6X10⁸ ) = 600000000

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 example, the face value of 2 is 2, the face value of 3 is 3 and so on.

TYPES OF NUMBERS:

Natural Numbers : Counting numbers 1, 2, 3, …. are called Natural Numbers.

Whole Numbers: All Counting numbers together with zero form the set of Whole Numbers. Thus,

• 0 is the only whole number which is not a natural number.
• Every natural number is a whole number.

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.

‘0’ is neither positive nor negative. So {0, 1, 2, 3,…} represents non-negative integers, while {0, -1, -2, -3 ….} represents the set of non-positive integers.

Even Numbers: A number divisible by 2 is called an even number. (Eg.) 2, 4, 6, …..

Odd Numbers: A number not divisible by 2 is called an odd number. (Eg.) 1, 3, 5, …..

Prime Numbers: A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself. Two numbers are said to be Co-Primes, if their H.C.F. is 1. Eg. : (2,3), (7,9), etc.,

Composite Numbers: Numbers greater than 1 which are not prime, are known as composite numbers. (Eg.) 4, 6, 8, 9, 10

• 1 is neither prime nor composite.
• 2 is the only even number which is prime.
• There are 25 prime numbers between 1 and 100.

Prime numbers upto 100 : 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.

How can we find prime numbers Greater than 100? :

Let p>100, First find a whole number nearly greater than the square root of p. Let k be the number which is greater than square root of p. Test whether p is divisible by any prime number less than k. If yes, then p is prime. Otherwise p is not prime.

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