Difference between Rational & Irrational Numbers

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).

Major differences between these two terms are mentioned below: 

Rational Numbers: 

• Numbers that can be expressed as a ratio of two number (p/q form) are termed as a rational number.
• Rational Number includes numbers, which are finite or are recurring in nature.
• Rational Numbers includes perfect squares such as 4, 9, 16, 25, and so on
• Both the numerator and denominator are whole numbers, in which the denominator is not equal to zero.
• Example: 3/2 = 1.5, 3.6767

Irrational Numbers: 

• Numbers that cannot be expressed as a ratio of two numbers are termed as an irrational number.
• These consist of numbers, which are non-terminating and non-repeating in nature.
• Irrational Numbers includes surds such as √2, √3, √5, √7 and so on.
• Irrational numbers cannot be written in fractional form.
• Example: √5, √11