Types of Numbers: Overview, Questions, Preparation

Number System 2021 ( Maths Number System )

Rajdeep Das
Updated on Sep 6, 2021 02:02 IST

By Rajdeep Das

Table of content
  • Types of Numbers
  • Natural Numbers
  • Properties of natural numbers
  • Real Numbers
  • Properties of real numbers
  • Rational Numbers
  • Properties of rational numbers:
  • Irrational Numbers
  • Properties of Irrational Numbers
  • Imaginary Numbers
  • Properties of Imaginary Numbers
  • Illustrated Examples
View More
Maths Number System Logo

Types of Numbers

Based on their properties and how they are addressed in the number line, the numbers are divided into different types. Each classification of the number is provided with its description, the properties, and the examples to understand it better. The different types of numbers are:

Maths Number System Logo

Natural Numbers

Natural Numbers are also termed as “counting numbers”, which contain a series of positive integers of 1 to unlimited. The number of natural numbers is represented by the letter "N". The game of natural numbers is defined by:

N = {1, 2, 3, 4, 5, … .} 

Maths Number System Logo

Properties of natural numbers

  • The addition of natural numbers is closed, associative and commutative.
  • The natural number of multiplication is closed, associative and commutative.
  • The identity element of a natural number to the addition is zero.
  • The identity element of a natural number under multiplication is one.
Maths Number System Logo

Real Numbers

Any number such as positive integers, negative integers, fractional numbers or decimal numbers without imaginary numbers are called the actual numbers. It is represented by the letter "R". It is represented by the letter "R."

Models: ¾, 0.333, √2, 0, 10, 20, etc.

Maths Number System Logo

Properties of real numbers

  • The actual numbers are commutative, associated, and distributive under addition and multiplication.
  • The actual figures obey the reverse property.
  • The additive and multiplicative identity elements of real numbers are 0 and 1, respectively.
Maths Number System Logo

Rational Numbers

Any written number in the form of P / Q, that is to say, that a ratio of a number on another number is called digital rational. A rational number can be represented by the letter "Q".

Models: 7/1, 10/2, 1/1, 0/1, etc.

Maths Number System Logo

Properties of rational numbers:

  • The rational figures are closed under addition, subtraction, multiplication, and division.
  • It satisfies the commutative goods and is associated with addition and multiplication.
  • It obeys a distributive property to add and subtract.
Maths Number System Logo

Irrational Numbers

The number that cannot be expressed in the form of P / Q. This means a number that cannot be written because the report of another is called irrational numbers. It is represented by the letter "p".

Models: √2, π, Euler's steady, and so on 

Maths Number System Logo

Properties of Irrational Numbers

  • The irrational numbers do not satisfy the closing property.
  • It obeys a commutative and associative property under addition and multiplication.
  • The irrational numbers are distributive under addition and subtraction.

Models: 4 + 4i, - 2 + 3i, 1 +√2i, and so on

Read more
Maths Number System Logo

Imaginary Numbers

Imaginary numbers are classified under complex numbers. This is the product of real numbers with the imaginary unit "I". The imaginary part of the complex numbers is defined by IM (Z).

Models: √2, i2, 3i, and so forth 

Read more
Maths Number System Logo

Properties of Imaginary Numbers

The imaginary numbers have an interesting property. It cycles through 4 different values ​​each time when it is under a multiplication operation.

  • 1 × I = I = I
  • I × I = -1
  • -1 × i = -i
  • -I × I = 1
Read more
Maths Number System Logo

Illustrated Examples

1. ⅗ is which kind of number?

The integers are whole numbers. 35 is a rational number because it represents a ratio of two integers.

2. What kind of number is 21?

Number 21 is a rational number. It is an integer or an integer, and all integers are rational numbers.

3. √21 is which kind of number?

It is an irrational number.

FAQs

Q: Which number is rational? √5 or √196?

A: √196= 14, so it will be a rational number

Q: Which number is irrational? √2 or √71?

A: √2 will be an irrational number

Q: If "m" lies between 30 and 40, then the value of "m" will be where it will be an integer.

A: Their square base of m is an integer, so m is a square number somewhere in the range of 30 and 40 Subsequently, m is 36 as this is the square number it will be √36=6

Q: Which number will be in between 1 and 2?

A: √2

Q: What kind of number is zero?

A: Zero is a rational, whole, integer and real number.
Read more
qna

Maths Number System Exam

Student Forum

chatAnything you would want to ask experts?
Write here...