Mathematics

Difference between Rational and Irrational Numbers

the basic difference between Rational and Irrational Numbers is that rational numbers are those which can be expressed as p/q form where p,q both are integers and always q≠0 while irrational numbers are those which cannot be written as p/q form where p and q are integers and q≠0. the rational and irrational both are real numbers.

In this article, you are going to learn a complete explanation about the Difference between Rational and Irrational Numbers.

This Article Also includes:

  • Overview
  • What is a Rational number?
  • What is an Irrational number?
  • Examples of both
  • Lots more…!

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Let’s Dive right in…!

Overview

most people often confuse while identifying these numbers. the easy way to differentiate between both is that rational numbers and irrational numbers both are composed of integers but the first one can be written as p/q form and the last one cannot do so.

what does that mean by p/q?

for example, we have 6/3=2, which is a proper fraction. hence, it can be solved as p/q and is said to be a rational number. in another example, we have √11 which cannot be divided properly. hence √11 is an irrational number that cannot be written as p/q form.

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Difference between Rational and Irrational Numbers in Tabular Form

Rational

Irrational

those numbers can be written in form of p/q or a ratio of two numbers. those numbers cannot be written in form of p/q or a ratio of two numbers.
for example: 3/2= 1.5, 8.4, 6.6, etc. for example √7=2.64, √11, etc.
they are always are recurring in nature or finite. they are always non-terminating and non-repeating in nature.
numerator and denominator belong to whole numbers and the denominator is not equal to zero. they cannot be written in fractional form.
they are always perfect squares for example 4, 16, 25 25, 9, and so on. they are always surds for example √2, √7, √11, √3, √5,  and so on.

What is a Rational Number?

The number consisting of integers that can be expressed as p/q form known as a rational number. It is denoted by (Q) which lies in real numbers (R) while their participant integers (Z) are known as natural numbers (N). In this case, the integers consist of two parts denominator q, which cannot be zero, and numerator p.

every participant integer also belongs to rational numbers for example 7=7/1. the p/q expression ends into a finite number of digits or it shows a repeated pattern or sequence.

so, if the repeating or terminating decimal series is known as a rational number. similarly, the addition and multiplication of different integers of a rational number also turn into a rational number.

The terminology of Rational numbers

What is an Irrational Number?

irrational numbers are those which are not rational and also belongs to the real numbers. these numbers cannot be expressed as the ratio of two integers. a common example of these numbers is √3, √2, etc. other than that, all square roots of natural numbers, other than of perfect squares, are irrational.

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