Formula To Solve Number System Questions

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.