Math's: Number System: Introduction, Natural Numbers, Whole Numbers and Integers

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Introduction

Number System is a writing way to represent numbers. It represents a set of numbers that consist of natural numbers, integers, whole numbers, rational numbers etc.

Natural Numbers

The numbers we use for counting i.e. so on constitute natural numbers. 1 is the smallest natural number and there is no greatest natural number.

Natural Numbers Have Some Basic Properties

1. When two natural numbers are added, the resultant number is also a natural number.

Ex- . we see 7 is a natural number

2. When two natural numbers are multiplied, the result is also a natural number.

Ex- . we see 12 is a natural number

3. When one natural number is subtracted from another, the result may or may not be natural number

Ex (i) . Here 1 is a natural number

(ii) . Here -4 is not a natural number

4. When one natural number is divided by another, the resultant number may or may not be a natural number.

Ex (i) . Here 2 is a natural number

(ii) is not defined in a natural number

5. The natural numbers can be represented on a number line as given below:

Natural Numbers

Natural Numbers

Two natural numbers can be added and multiplied in any order and the result obtained is always same. This does not hold true for subtraction and division of natural numbers.

Whole Numbers

  • The set of all-natural numbers along with 0 (zero) are whole numbers. Thus, the whole numbers are-

  • so on.

  • 0 is the smallest whole number and there is no greatest whole number.

  • Whole numbers have the same basic properties as those of the natural numbers (given above from 1 to 6).

  • The whole numbers can also be represented on a number line as given below:

Whole Numbers

Whole Numbers

The Whole Number 0 Has Some Special Properties

1. When zero is added to any whole number say a, the result is the number itself.

i.e.

2. When zero is subtracted from any whole number say a, the result is the number itself.

i.e.

3. When zero is multiplied by any whole number say a, the result is zero.

i.e.

Integers

  • Integers comprise of all whole numbers and their negative opposites.

  • The integers therefore are:

  • The numbers having no sign (or positive sign) are known as positive integers.

  • The numbers having negative signs are negative integers

  • Like natural numbers and whole numbers, integers can also be represented on number line as shown below:

Number System: Integers

Number System: Integers

It is to be noted that the integers lying on the right side of the number line are greater than those on the left side. if an integer , then will always be to the right of , otherwise vise-versa.

1. State which of the following are natural numbers, whole numbers and negative integers:

(i) 75

(ii) -17

(iii) 0

(iv) 34

(v) 4

(vi) -12

(vii) 120

(viii) -2

Solution: Natural Numbers- (i), (iv), (v), (vii)

Whole Numbers- (i), (iii), (iv), (v), (vii)

Negative Integers- (ii), (vi), (viii)

2. Simply the following and state whether the result is a positive integer or not.

(i)

(ii)

(iii)

(iv)

Solution: (i)

(ii)

(iii)

(iv)

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