Number Types

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Types of Numbers in Math

Just like different individuals of the same family live in different homes, different numbers belong to the same family but have different types. Over time, various patterns of ten digits have been categorized into an array of number types. This framework of numbers varies from each other because of different properties and presentations.

That said, the types of numbers in maths are classified as per some purpose that they serve, property that they possess or fundamental rule that they follow.

What Are Numbers?

Those ten elegant digits, symbols, or numerals that we all learn early in life are the numbers. Numbers are algebraic in form and have a greatest influence in our lives in far more ways than we could ever think of.

Numbers in Real Life

Ever wondered what our lives would be like in absence of these 10 digits and the innumerable array of other numbers that they can create? Numbers are everywhere in our birth dates, ages, height, weight, addresses, phone numbers, credit card numbers, bank account numbers and a lot more.

Classification of Numbers

Numbers family can be classified in different categories. With that, we can also say that two or more types of numbers in maths can fall under one category. Refer to the image below for complete understanding of classification of numbers:

(Image to be added soon)

Different Types of Numbers

There are various types of numbers in maths. Let’s discuss some of the following:

  1. Natural Numbers - the set of numbers, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 that we see and use in our routine life. The natural numbers are commonly known as positive integers and counting numbers.

  2. Whole Numbers - the natural numbers plus (+) the zero (0).

  3. Real Numbers - set of real numbers in addition to all the rational and irrational numbers and are represented by the letter R. It also includes all the numbers that can be written in the decimal form.

  1. Fractional Numbers - any number expressible by the quotient of two numbers as in m/m, "m" greater than 1, in which "m" is the numerator and "n" is the denominator.

  2. Irrational Numbers - any number that is unable to be expressed by an integer or the ratio of two integers. These numbers are expressible only as decimal fractions in which the digits are ongoing with no repeating pattern. Examples of irrational numbers are √2 , √3.

  3. Transcendental Numbers - any number unable to be the root of a polynomial equation with rational coefficients.

Quantum Numbers

Set of numbers used to define the energy and position of the electron in an atom are known as quantum numbers. 

Types of Quantum Numbers

There are four quantum numbers that define the probable location of an electron in an atom which are as given:

  • The Azimuthal Quantum Number denoted by symbol ‘l’

  • The Magnetic Quantum Number denoted by symbol ‘ml’

  • The Principal Quantum Number denoted by symbol ‘n’

  • The Spin Projection Quantum Number denoted by symbol ‘ms’

Fun Facts

  • Almost all of us whether mathematicians, scientists, doctors, engineers, manufacturers, cashiers or carpenters could not survive without numbers.

  • Zero(0) as a number has the greatest value and importance.

Solved Examples


Find out the square root of -16? Write your answer in the form of imaginary number i.


Step 1: Write the number in terms of square root √ (-16)

Step 2: Separate out -1. √ (16 × -1)

Step 3: Move apart square roots.√ (16) × √ (-1)

Step 4: Solve and simplify the square root. 4 × √ (-1)

Step 5: Write in mathematical terms of i.4i

Sometimes you get an imaginary solution to the equations.

Example 2

Simplify and solve the equation: a2 + 2 = 0

Step 1: Take the constant term on other side of the linear expression: a2 = -2

Step 2: Take the square root on both sides of the equation √a2 = +√-2 or -√-2

Step 3: Solve and simplify: a = √ (2) × √ (-1)

                        a = +√2i or -√2i

Step 4: Double check the answers by substituting values in the initial equation and see if we obtain 0. a2 + 2

(+√2i) 2 + 2 = -2 + 2 = 0   [since i = √-1 and square of i will be -1]

(-√2i) 2 + 2 = -2 + 2 = 0 [since i = √-1 and square of i will be -1]


we would not be able to live without numbers in our lives. Interestingly, there exists an almost infinite array of number types and hidden wonders emanating from these acquainted symbols that we use every day, the natural numbers.

FAQ (Frequently Asked Questions)

1. What are imaginary numbers and its applications?

Just because their name is “imaginary” does not mean they are purposeless. They have several applications. In a few places, the imaginary number is also denoted by the letter ‘j’. One of the substantial applications of imaginary numbers is its wide application in electric circuits. The computations of current and voltage are carried out with respect to imaginary numbers. Imaginary numbers also have different applications in fields like systems, signals and fourier transform. These numbers are also frequently used in complex calculus calculations.

2. What are rational numbers and its applications?

Rational numbers are ones which can be mathematically expressed in the form of fraction. The term “rational” originates from the term, “ratio”, as rational numbers are the ratios of the 2 integers. Rational numbers are denoted by the letter ‘Q’. For example, 0.9 is a rational number since this can be written as 9/10. Other examples of rational numbers are -2/5, 1/3, 79/80, 1.57, etc.

Assume a rational number x/y, where x and y are two integers. Here, the numerator x can be any integer (positive or negative), but the denominator y can never be 0, since the fraction is unspecified then. Moreover, if y = 1, then the fraction will be an integer.

3. What are the types of rational numbers?

Rational Numbers can be in the form of whole numbers like (0, 1, 2, 3, 4, 5 ...), the integers (.-1, - 2, - 1, 0, 1, 2 ...), fractions (2/3) and repeating and terminating decimals.