The key difference between rational and irrational numbers is, the rational number is expressed in the form of p/q whereas it is not possible for irrational number (though both are real numbers). Learn the definitions, more differences and examples based on them.
Definition of Rational and Irrational Numbers
Rational Numbers: The real numbers which can be represented in the form of the ratio of two integers, say P/Q, where Q is not equal to zero are called rational numbers.
Irrational Numbers: The real numbers which cannot be expressed in the form of the ratio of two integers are called irrational numbers.
What is the Difference Between Rational Numbers and Irrational Numbers?
| S.No | Rational Numbers | Irrational Numbers |
| 1 | Numbers that can be expressed as a ratio of two numbers (p/q form) are rational numbers. | Numbers that cannot be expressed as a ratio of two numbers are irrational numbers. |
| 2 | The decimal expansion of rational numbers is either terminating or recurring. | The decimal expansion of irrational numbers is non-terminating and non-recurring. |
| 3 | Rational numbers include perfect squares such as 4, 9, 16, 25, and so on. | Irrational numbers include surds such as √2, √3, √5, √7 and so on. |
| 4 | Both the numerator and denominator are integers, in which the denominator is not equal to zero. | Irrational numbers cannot be written in fractional form. |
| 5 | Example: 3/2 = 1.5, 3.6767 | Example: √5, √11 |
Video Lesson on Rational Numbers
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Frequently Asked Questions – FAQs
Q1
What is the main difference between rational and irrational numbers?
We can represent rational numbers in the form of the ratio of two integers(positive or negative), where the denominator is not equal to 0. But we cannot express irrational numbers in the same form.
Q2
Give examples of rational and irrational numbers.
Examples of rational numbers are 1/2, 3/4, 11/2, 0.45, 10, etc.
The examples of irrational numbers are Pi (π) = 3.14159…., Euler’s Number (e) = (2.71828…), and √3, √2.
The examples of irrational numbers are Pi (π) = 3.14159…., Euler’s Number (e) = (2.71828…), and √3, √2.
Q3
How can we identify if a number is rational or irrational?
If a number has a terminating or repeating decimal, it is rational; for example, 1/2 = 0.5.
If a number has a non-terminating and non-repeating decimal, it is irrational, for example, o.31545673…
If a number has a non-terminating and non-repeating decimal, it is irrational, for example, o.31545673…
Q4
Is 2/3 rational or irrational?
2/3 = 0.66666…
We can see, after simplification, 2/3 is a repeating decimal. Hence, it is a rational number.
We can see, after simplification, 2/3 is a repeating decimal. Hence, it is a rational number.
A non terminating decimal fraction whose decimal part contains digits which are repeated again and again in the same order is called a recurring decimal fraction. All such fractions can be converted to the form p/q so they are rational numbers.