Difference between Rational & Irrational Numbers

Mathematics involves numbers, proofs, theorems, which are applied to study the topic such as quantity, space, structure and change. Just think of your date of birth, doesn’t it involves the use of mathematics?

We use of mathematics in our everyday life, such as in purchasing goods, the money we have etc. Numbers are involved in our day-to-day life.

In the classification of numbers, Rational and Irrational numbers plays a lot of confusion to many students. So here we provide the detailed explanation to these numbers which is easy to remember. Let us have a comparison of Rational & Irrational Numbers-

Comparison of Rational & Irrational Numbers-

(i) Basic Definition-

  • Rational Numbers- A number that can be expressed as a ratio of two number (p/q form) are termed as Rational Number.
  • Irrational Numbers- A numbers that cannot be expressed as a ratio of two numbers are termed as Irrational Number.

(ii) Decimal Form/type-

  • Rational Number- Rational Number includes numbers, which are Finite or are recurring in nature.
  • Irrational Number- These consist of numbers, which are non-terminating and non-repeating in nature.

(iii) Eg-

  • Rational Numbers- \(1. 5 = \frac{3}{2}\), \(0.16666…… = \frac{15}{90} = \frac{1}{6}\)

Learn the basic conversion of Repeating decimal to fraction.

  • Irrational Numbers- \(\sqrt{5}, \sqrt{11}\) etc.

Practise This Question

Collinear vectors need to have same direction