# Formula To Solve Number System Questions

## Formulas to Solve Number System

Number system is a writing system for presenting number on the number line. A number system is a system of writing or expressing numbers.
There are generally two type of Number (i) Whole Number (ii) Natural Number.

## Number System Formulas & Definitions

### Natural Numbers

All positive integers are called natural numbers. All counting numbers from 1 to infinity are natural numbers.
N = {1, 2, 3, 4, 5, 6……….∞}

### Whole Numbers

The set of numbers that includes all natural numbers and the number zero are called whole numbers. They are also called as Non-negative integers.
W = { 0,1,2,3,4,5,6,7,8,…………..∞}

### Integers

All numbers that do not have the decimal places in them are called integers.
Z = {∞…….-3, -2, -1, 0, 1, 2, 3………∞}
a. Positive Integers: 1, 2, 3, 4….. is the set of all positive integers.
b. Negative Integers: −1, −2, −3….. is the set of all negative integers.
c. Non-Positive and Non-Negative Integers: 0 is neither positive nor negative.

### Real Numbers

All numbers that can be represented on the number line are called real numbers.

### Rational Numbers

A rational number is defined as a number of the form a/b where ‘a’ and ‘b’ are integers and b ≠ 0. The rational numbers that are not integers will have decimal values. These values can be of two types
a. Terminating decimal fractions: For example: 1/5 = 0.5, 125/4 = 31.25
b. Non-Terminating decimal fractions: For example: 19/6 = 3.1666666, 21/9 = 2.33333

### Irrational Numbers

It is a number that cannot be written as a ratio x/y form (or fraction). An Irrational numbers are non-terminating and non-periodic fractions. For example: √2 = 1.414

### Complex Numbers

The complex numbers are the set {a+bi}, where, a and b are real numbers and ‘i’  is the imaginary unit.

### Imaginary Numbers

A number does not exist on the number line is called imaginary number. For example square root of negative numbers are imaginary numbers. It is denoted by ‘i’ or ‘j.

### Even Numbers

A number divisible by 2 is called an even number. For example: 2, 6, 8, 14, 18, 246, etc.

### Odd Numbers

A number not divisible by 2 is called an odd number. For example: 3, 7, 9, 15, 17, 373, etc.

### Prime numbers

A number greater than 1 is called a prime number, if it has exactly two factors, namely 1 and the number itself. For example: 2, 3, 5, 7, 11, 13, 17, etc.

### Composite numbers

Numbers greater than 1 which are not prime, are known as composite numbers. For example: 4, 6, 8, 10, etc.

### Formulas for Number System and Basic Concept

• (a – b) = (a² – b²)
• (a + b)² = (a² + b² + 2ab)
• (a – b)² = (a² + b² – 2ab)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (a³ + b³) = (a + b)(a² – ab + b²)
• (a³ – b³) = (a – b)(a² + ab + b²)
• (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
• When a + b + c = 0, then a³ + b³ + c³ = 3abc. 