Complete Lesson on Types of Numbers

Can you think of just how your life would be if you did not have any way to represent weight, ages, birthdays, scores, time, checking account, and phone number? The ten digits (0 to 9) are utilized to define all of these types of numbers.

Numbers are strings of numbers used to stand for an amount. The size of a number suggests the dimension of the quantity. It can be either huge or tiny. They exist in different kinds, such as 3, 999, 0.351, 2/5, etc.

Types of Numbers in Mathematics

Like various persons of the very same family members reside in different homes, different numbers are of the same household but have different kinds. Over time, multiple patterns of 10 digits have been categorized into a category of number types. These patterns of numbers are different from each other because of their various representations and properties.

Natural Numbers

All-natural numbers or counting numbers are the most fundamental numbers that you discovered for the first time as a kid. They initiate from 1 and go to infinity, i.e. 1, 2, 3, 4, 5, 6, and more. They are also called positive integers. In the standard operating procedure, they can be created as:

1,2,3,4,5 …

All-natural numbers are represented by icon N.

Whole Numbers

Digits are the collection of all-natural numbers, consisting of no. This means they begin with 0 as well as rise to 1, 2, 3, and so forth, i.e.

Whole numbers are represented by the sign W.


They are the set of all whole numbers and negatives of all-natural numbers. It consist of all the digits which lie between negative infinity as well as positive infinity. They can be positive, absolutely no, or negative, yet cannot be written in decimal or fraction. Integers can be written in standard operating procedure as

…, -3, -2, -1, 0, 1, 2, 3, …

We can claim that all whole numbers and also natural numbers are integers, but not all integers are all-natural numbers or whole numbers.

Integers are stood for by the symbol Z.


A fraction stands for parts of a whole number. We can also write it in the form a/b, where both an and b are whole numbers, and b can never amount to 0. All portions are reasonable numbers, yet not all rational numbers are portions.

Fractions are further minimized to appropriate as well as inappropriate portions. Improper fractions are defined as when the numerator is greater than the reverse is accurate in proper functions, i.e. denominator is more than the numerator. Instances of appropriate fractions are 3/7 and 99/101, while 7/3 and 101/99 are incorrect fractions. This means the improper fractions are always more than 1.

All terminating decimals, as well as repeating decimals, can be created as fractions. It can make the ending decimal 1.25 as 125/100 = 5/4. A duplicating decimal 0.3333 can be composed as 1/3.

Rational Numbers

They are the ones who are represented in portion form. Words “rational” are derived from the words “proportion,” as rational numbers represent the two integers’ proportions. For instance, 0.7 is a rational number because it can be created as 7/10. Various other examples of reasonable numbers are -1/ 3, 2/5, 99/100, 1.57, and so on.

Take into consideration a logical number p/q, where p and q are two integers. Right here, the numerator p can be any integer (positive or negative), yet the denominator q can never be 0, as the fraction is undefined after that. Also, if q = 1, then the portion is an integer.

Rational numbers are stood for by the symbol Q.

Irrational Numbers

You cannot write irrational numbers in portion form, i.e., they can not be written as the proportion of both integers. A couple of examples of irrational numbers are √ 2, √ 5, 0.353535 …, π, and so forth. You can take a look at the digits in irrational numbers continue for infinity without duplicating pattern.

Irrational numbers are stood for by the symbol Q.

Real Numbers

Real numbers are the set of all reasonable and also Irrational numbers. This includes all the numbers which can be written in the decimal type. All integers are genuine numbers, however not all actual numbers are integers. Real numbers consist of all the integers, digits, fractions, repeating decimals, terminating decimals, and so on.

The symbol R represents genuine numbers.

Types of Numbers: Imaginary Figures

Numbers aside from real numbers are Imaginary or complex numbers. When we settle a fictional number, it provides an unfavourable result, which means it is a square origin of a negative number, for instance, √ -5 and √ -2. When we square these figures, the outcome is -5 as well as -2. The Negative one’s square root is represented as:

i = √ -1.

Example 1.

What is the square root of -16? Create your answer in terms of the imaginary number i.


Step 1: Create a square origin kind.

√( -16 ).

Step 2: Separate -1.

√( 16 × -1).

Action 3: Different square origins.

√( 16) × √( -1 ).

Tip 4: Fix the square root.

4 × √( -1 ).

Tip 5: Write in the form of i.


Occasionally you obtain an imaginary remedy to the equations.