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 number (p/q form) are termed as a rational number. | Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number. |
| 2 | Rational Number includes numbers, which are finite or are recurring in nature. | These consist of numbers, which are non-terminating and non-repeating in nature. |
| 3 | Rational Numbers includes perfect squares such as 4, 9, 16, 25, and so on | Irrational Numbers includes surds such as √2, √3, √5, √7 and so on. |
| 4 | Both the numerator and denominator are whole numbers, 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 |
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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 ratio of two integers(positive or negative), where denominator is not equal to 0. But we cannot express irrational numbers in the same form.
Q2
Give an example of rational and irrational numbers?
The 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 is terminating number or repeating decimal, then it is rational, for example, 1/2 = 0.5.
If a number is non-terminating and non-repeating decimal, then it is irrational, for example, o.31545673…
If a number is non-terminating and non-repeating decimal, then 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.