Concepts of Number System

We will will looking at the types of numbers like natural numbers, whole numbers, integers, prime and composite numbers etc. and basic concepts of number system. 

Let’s begin –

Concepts of Number System

Natural Numbers and Whole Numbers

Natural numbers, also called counting numbers, are the first numbers we learnt. They are the number set 1, 2, 3, 4 ….. \(\infty\).

On the other hand, whole numbers is the set of natural numbers plus, the number zero.

Thus, 0,1, 2, 3, 4 ….. \(\infty\) is the set of whole number.

Integers and Decimals

All numbers that don not have a decimal in them are called integers. Thus -3, -17, + 4, +13, +1473, 0 etc are all integers.

Obviously, decimal numbers are numbers which have a decimal value attached to them. Thus, 1.3, 14.76, -12,24 etc are all decimal numbers, since they have certain values after the decimal point.

Prime Numbers

These are numbers which have no divisors/factors apart from 1 and itself. Thus, 2, 3, 5, 7, 11 etc are all prime numbers.

Composite Numbers

The numbers which have atleat one more divisor apart from 1 and itself are called composite numbers.

Note : A breif word about factors/division – A number is said to be divide Y ( or is said to be a divisor or factor of Y). When the division of Y/X leaves no remainder.

All composite numbers have the property that they can be written as the product of ther prime factors.

Thus, 4, 6, 8, 9, 10 etc are all composite numbers.

Rational and Irrational Numbers

Numbers which can be expressed in the form p/q where q \(\ne\) 0 are called rational numbers. For example, 4.2 can be written as 42/10 and then converted to 21/5. Hence it is a rational number

Other example is 4.333…. which can be written as 13/3 is also a rational number

Obviously, numbers which cannot be represented in the form p/q are called as irrational numbers.

For example, \(\sqrt{3}\), \(\sqrt{7}\) are irrational numbers.

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