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 involve the use of Mathematics?

We use 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 play a lot of confusion to many students. So here we provide a detailed explanation to these numbers which is easy to remember. Let us discuss the difference between the rational and irrational number in detail.

Key Differences Between Rational 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, 1/ 6 =0.1666.. Example: √5, √11

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