Real Number Definition

It is the union of Rational and Irrational numbers. The set of real numbers includes all those numbers that we use in our daily life. In Mathematics, Real numbers are represented by “R”.

For example, -3, 2, 22/7, etc are all real numbers.

In this set of numbers, all digits, fractions, and decimals are included unless an imaginary part appears. A term is called an imaginary number if a negative sign comes with the number under the radical sign.


Read about Imaginary Numbers here.

Major Types of Real Numbers

In Mathematics, Real Numbers are divided into two major groups. As mentioned above, it is the union of Rational and Irrational numbers. So, these sets are two major types of this set.

• Rational Numbers

All those numbers can be written in a defined fraction. For example, 1/9 is a rational number as it has a definite numerator and denominator.

• Irrational Numbers

All those numbers can’t be written in a defined fraction. For example, 3.14159…. is an irrational number because we can write it in a definite fraction.


You can read about Rational & Irrational numbers.

List of Sets Including Real Numbers

As the name shows, all real numbers will come under this section. Let us show you the most common sets of Mathematics that are part of Real numbers.

These all sets are part of a single set that is called Real Numbers.

Properties that Hold in Real Numbers

In Mathematics, every set of numbers fulfills some properties or we can say that some properties hold for a specific set of numbers. Similarly, some properties also hold for Real Numbers. Here is the list of those properties that hold for this.

  • Commutative Property
  • Associative Property
  • Distributive Property
  • Identity Property

Real Numbers Chart


Is Pi a real number?

Yes, Pi is a real number as it is part of a set of irrational numbers.

Which numbers are not considered real numbers?

All those numbers that have an imaginary portion will not be part of the set of real numbers.

Is a rational number a subset of real numbers?

Yes, rational and irrational numbers are two major subsets of real numbers.

Is a real number a subset of a complex number?

It can be said that a real number is a subset of complex numbers because a complex number has two main portions named real part and the imaginary part.

Is “0” a real number or a complex number?

“0” is part of a real number as it is part of whole numbers. It is not a complex number because there is no imaginary part attached to this number.

What is the difference between whole numbers and real numbers?

A real number includes all numbers that we use in our daily life including negative numbers while a set of whole numbers include only positive numbers with 0. We can say that the set of whole numbers is a subset of real numbers.