# Number Systems

#### Number Systems

Number: Arithmetical value representing a particular quantity. The various types of numbers are Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers etc.

### Natural Numbers

Natural numbers(N) are positive numbers i.e. 1, 2, 3 ..and so on.

### Whole Numbers

Whole numbers (W) are 0, 1, 2,..and so on. Whole numbers are all Natural Numbers including ‘0’. Whole numbers do not include any fractions, negative numbers, or decimals.

### Integers

Integers are the numbers that include whole numbers along with negative numbers.

### Rational Numbers

A number ‘r’ is called a rational number if it can be written in the form p/q, where p and q are integers and q ≠ 0.

### Irrational Numbers

Any number that cannot be expressed in the form of p/q, where p and q are integers and q≠0, is an irrational number. Examples: √2, 1.010024563…, e, π

### Real Numbers

Any number which can be represented on the number line is a Real Number(R). It includes both rational and irrational numbers. Every point on the number line represents a unique real number.

### Imaginary Numbers

Imaginary numbers are those numbers which we can just imagine but cannot physically perceive.

For Example √-1, √-3, etc, √-1 is represented by i, Square Root of all imaginary number is imaginary.

### Complex Number

The combination of Real and Imaginary numbers is called complex numbers. Example: (2+5i) , (1+3i) etc.

### Even number

An integer that is “evenly divisible” by two. Example 2,4,8,….. etc.

### Odd number

All the Natural numbers which are not Even numbers. Example 1, 3, 19, 21,….. etc.

### Prime number

An integer is greater than 1 which is only divisible by 1 and the number itself are called prime numbers. Example 2,3,5,7,11,13,….etc

### Co-Prime Number

If the only positive integer (factor) that divides both of them is 1. Examples:- 13 and 14 are co-prime, being commonly divisible only by 1, while 22 and 24 are not co-prime because they are both divisible by 2.

### Composite Number

All the natural numbers greater than 1 which are divisible by at least one more number other than 1 and the number itself are called composite numbers. Example: 6 can be divided exactly by 3 or 2 (as well as 1 and 6), so 6 is a composite number. But 7 cannot be divided exactly (except by 1 and 7), so is NOT a composite number (it is a prime number).

### Place value

The place or position of a digit in a number is called its place value. Example: Place value of 2 in 4289 is 200.

### Face value

The real value of any digit in a certain number is called its face value.

For example, the face value of 2 in 7246 is 2.