Numbers

A number is a smallwst unit of calculation. we have ten digist which comprises unlimited numbers. These ten digits are 0, 1 2, 3, 4, 5, 6, 7, 8, and 9. There are two types of values of these numbers. Place value and Face value.

  Place value  

As the name shows place value, the value oa a number at which it is placed. It values is determined in 'ones', 'tens', 'hundreds' and so on. For example, we have a number 457836. The number will be read as 4 Lakh, fifty seven thousand, eight hundred, and thirty four. The place value in the above number is fourth which determmine that its place value is in thousands. Similarly the digit 5 is at fifth place which determines that its place value is in ten-thousands. 4 is placed at sixth which determine that the place value of 4 is in lakhs.

  Face value  

Face value is simply the value of a number. In above example we have a number 457836. The place value of '6' is 'one' but its face value is '6'. the pace value of '8' is three and the face value of 8 is '8'.

Various Types of Numbers

  1. Natural Numbers: Counting numbers are called natural numbers.

Thus 1, 2, 3, 4,………… are all natural numbers.

  1. Whole Numbers; all counting numbers, together with 0, from the set of whole numbers.

Thus , 0, 1, 2, 3, 4,…….. are all whole numbers.

  1. Integers: All counting  numbers, zero and negatives of counting numbers, form the set of integers.

Thus,……,-3, -2, -1, 0, 1, 2, 3,……… are all integers.

Set of positive integers = { 1, 2, 3, 4, 5, 6……..}

Set of negative integers ={ -1, -2 , -3, -4, -5, -6…….}

Set of all non-negative integers = {0, 1, 2, 3, 4, 5……}

  1. Even Numbers: A counting number divisible by 2 is called an even number.

Thus, 0, 2, 4, 6, 8, 10,12,……etc. are all even numbers.

  1. Odd Numbers: A counting number not divisible by 2 is called an odd number.

Thus, 1, 3, 5, 7, 9, 11, 13,……etc. are all odd numbers.

  1. Prime Numbers: A counting number is called a prime number if it has exactly two factors, namely itself as:

Ex. All prime numbers less than 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

  1. Composite Numbers: All counting numbers, which are nit prime, are called composite numbers.

A composite numbers has more than 2 factors.

  1. Perfect Numbers: A numbers, the sum of whose factors ( except the number itself ), is equal to the number, is a perfect number, e.g. 6, 28, 496

The factors of 6 are 1, 2, 3 and 6.And , 1+2+3 = 6.

The factors of 28 are 1, 2, 4, 7, 14 and 28. And , 1+2+4+7+14 = 28.

  1. Co-primes (or Relative Primes ): Two numbers whose H.C.F is 1 are called co-prime numbers,

Ex. (2, 3), (8, 9) are pairs of co-primes.

  1. Twin primes: Two prime numbers whose difference is 2 are called twin-primes,

Ex. (3, 5) , (5 ,7), (11, 13) are  pairs of twin-primes.

  1. Rational Numbers: Numbers which can be expressed in the form p/q, where p and q are integers and q is called rational numbers.

Ex. (-8/11, 0, 6, 5(2/3) etc.

  1. Irrational Numbers: Numbers which when expressed in decimal would be in non-terminating and non-repeating form, are called irrational numbers.

Ex. √2,   √3 , √5 , √7 , π , e , 0.231764735…