# Number System

Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed as digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box. Number Systems comprise multiple types based on the base value for their digits.

What is the Number Line?

A Number line is a representation of Numbers with a fixed interval in between on a straight line. A Number line contains all the types of numbers like natural numbers, rationals, Integers, etc. Numbers on the number line increase while moving Left to Right and decrease while moving from right to left. Ends of a number line are not defined i.e., numbers on a number line range from infinity on the left side of the zero to infinity on the right side of the zero.

Positive Numbers: Numbers that are represented on the right side of the zero are termed as Positive Numbers. The value of these numbers increases on moving towards the right. Positive numbers are used for Addition between numbers. Example: 1, 2, 3, 4, …

Negative Numbers: Numbers that are represented on the left side of the zero are termed as Negative Numbers. The value of these numbers decreases on moving towards the left. Negative numbers are used for Subtraction between numbers. Example: -1, -2, -3, -4, …

### Number and Its Types

A number is a value created by the combination of digits with the help of certain rules. These numbers are used to represent arithmetical quantities. A digit is a symbol from a set 10 symbols ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.  Any combination of digits represents a Number. The size of a Number depends on the count of digits that are used for its creation.

For Example: 123, 124, 0.345, -16, 73, 9, etc.

### Types of Numbers

Numbers are of various types depending upon the patterns of digits that are used for their creation. Various symbols and rules are also applied on Numbers which classifies them into a variety of different types:

1. Natural Numbers: Natural Numbers are the most basic type of Numbers that range from 1 to infinity. These numbers are also called Positive Numbers or Counting Numbers. Natural Numbers are represented by the symbol N.

```Example: 1, 2, 3, 4, 5, 6, 7, and so on.
```

2. Whole Numbers: Whole Numbers are basically the Natural Numbers, but they also include ‘zero’.  Whole numbers are represented by the symbol W.

```Example: 0, 1, 2, 3, 4, and so on.
```

3. Integers: Integers are the collection of Whole Numbers plus the negative values of the Natural Numbers. Integers do not include fraction numbers i.e. they can’t be written in a/b form. The range of Integers is from the Infinity at the Negative end and Infinity at the Positive end, including zero. Integers are represented by the symbol Z.

```Example: ...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...
```

4. Fractions: Fractions are the numbers that are written in the form of a/b, where, a belongs to Whole numbers and b belongs to Natural Numbers, i.e., b can never be 0. The upper part of the fraction i.e. a is termed as a Numerator whereas the lower part i.e. b is called Denominator.

```Example: 1/2, 3/7, 8/3, etc.
```

5. Rational Numbers: Rational numbers are the numbers that can be represented in the fraction form i.e. a/b. Here, a and b both are integers and b≠0. All the fractions are rational numbers but not all the rational numbers are fractions.

```Example: -2/5, 0.54, 1/5, 13/4, ...
```

6. Irrational Numbers: Irrational numbers are the numbers that can’t be represented in the form of fractions i.e. they can not be written as a/b.

```Example: √2, √3, √.434343, π...
```

7. Real and Imaginary Numbers: Real numbers are the numbers that can be represented in the decimal form. These numbers include whole numbers, integers, fractions, etc. All the integers belong to Real numbers but all the real numbers do not belong to the integers.

Imaginary Numbers are all those numbers that are not real numbers. These numbers when squared will result in a negative number. The √-1 is represented as i. These numbers are also called complex numbers.

```Example: √-2, √-5,...
```

8. Prime Numbers and Composite Numbers: Numbers that do not have any factors other than 1 and the number itself are termed as Prime Numbers. All the numbers other than Prime Numbers are termed as Composite Numbers except 0. Zero is neither prime nor a composite number.

`Example: 2, 3, 5, 7,... are prime numbers and 4, 6, 8, 9, 12,... are composite number`
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