InMathematics, we need to come across lots that numbers. In these numbers, therecome perfect squares, surds, end decimals, non-terminating decimals,repeating decimals and also non-repeating decimal etc. We generally divide thesenumbers into two categories. The an initial category is known as rational numbersand the 2nd category is well-known as irrational numbers. No doubt, come understandthe difference between rational and also irrational numbers is a daunting task forthe students. Here, we will try to define the difference in between rational andirrational numbers through the help of examples.

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Difference in between the definitions of Rational and Irrational number

Definition of rational numbers

InMathematics, reasonable numbers space those numbers which space writtenin the type of p/q such that q≠0. The problem for the rational number isthat both p and also q should belong to Z and Z is a set of integers. The simplestexamples of the rational number are given below;


·10 or 10/1

Definition that Irrational number

Theirrational numbers are those numbers which space not written in the form of p/q.The simplest examples of the irrational number are given below;



Difference in between Rational and also Irrational numbers

Most that thestudents can’t understand the difference in between rational and also irrationalnumbers simply with the assist of your definitions. Castle require more detail tounderstand the difference in between rational and irrational numbers. The keydifference in between them is given below;

1. Perfect Squares space Rational Numbers and also Surdsare Irrational Numbers

All theperfect squares space rational numbers. The perfect squares space those numberswhich room the squares of one integer. In various other words, if we multiply one integerwith the same integer, we gain a perfect square. The instances of the perfectsquares space √ 4, √ 49, √ 324, √ 1089 and also √ 1369. After taking the square rootsof these perfect squares, we get 2, 7, 18, 33 and also 37 respectively. 2, 7, 18, 33and 37 room all integers.

On the otherhand, every the surds space the irrational numbers. Surds are those numbers whichare not the squares of one integer. In various other words, these space not the multiplesof one integer with itself. The examples of the surds are √2, √3 and also √7. Aftertaking the square roots of this surds, we obtain 1.41, 1.73 and also 2.64respectively. 1.41, 1.73 and also 2.64 room not integers.

2. End Decimals room Rational Numbers

All the terminatingdecimals are rational numbers. Terminating decimals are those decimal whichhave the finite number of digits ~ the decimal point. Because that example, 1.25,2.34 and 6.94 are all reasonable numbers. On the other hand, non-terminatingdecimals space those number which have actually the infinite variety of digits after ~ thedecimal point. Because that example, 1.235434..., 3.4444… and 6.909090… room allnon-terminating decimals. Non-terminating decimals can be rational orirrational. These are explained in the next point.

3. Repeating Decimals room Rational numbers andNon-Repeating Decimals space Irrational Numbers

All therepeating decimals room the rational numbers and the repeating decimal arethose decimals who digits repeat over and over again. The instances of therepeating decimals are .33333333, .222222 and also .555555. On the other hand, allthe non-repeating decimals room the irrational numbers and also the non-repeatingdecimals room those digits which don’t repeat over and over again. The examplesof the non-repeating decimals space .0435623, .3426452 and also .908612.


Types that Triangles v Pictures

Math Magic Tricks and also Questions

Key allude

The numberswhich space written there is no denominators room rational numbers. The instances ofthese type of numbers are 8 and also 9. This numbers space written in the kind ofp/q together 8/1 and 9/1. The numbers whose denominators room 0 are dubbed irrationalnumbers prefer 8/0 and 9/0.

Is ½ or 0.5 rational or Irrational Number?

0.5 iscalled the rational number since it have the right to be written in the form of p/q like5/10. Moreover, it is additionally a end decimal.

Is Pi (π) rational or Irrational Number?

Pi (π) is one irrational number. Its factor is thatit gives us non-repeating decimal 3.14159……

Is ‘0’ or ‘Zero’ reasonable or Irrational?

‘0’ or‘Zero’ is a reasonable number. Its factor is that ‘0’ or ‘Zero’ belongs come theset of integers and also we have questioned that every the integers room rationalnumbers.

Is it feasible for united state to discover Irrational Numbers between Two RationalNumbers?

It is easyfor us to uncover irrational numbers in between two rational numbers. We try to learnthis ide with the aid of one example. Find irrational numbers between 3 and4. We can uncover the irrational numbers in between these 2 rational numbers byfollowing these steps;

·Firstof all, we should discover squares of the offered numbers. In this case, the squaresof 3 and 4 room 9 and also 16 respectively.

·Secondly,you should uncover the prime numbers in between their squares. The prime numbersbetween 9 and 16 are 11 and 13.

·Bytaking the square root of this prime numbers, we acquire the required irrationalnumbers. The square roots of 11 and also 13 room 3.316624… and 3.6055512…respectively. As 3.316624… and 3.6055512… are non-repeating decimals. That’swhy these space irrational numbers.

Difference in Tabular type


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1SurdsPerfect Squares

Key point

You caneasily to express the rational number in the fraction form. ~ above the various other hand,you can’t to express the irrational numbers in the portion form. This is thebasic difference in between the rational and irrational numbers.

Practical examples

Afterunderstanding the difference between rational and irrational numbers, we try toseparate the rational and irrational number from offered numbers. Separate therational and irrational numbers from the following numbers;

√5, √25,5/4, 6/5, √36, √8, 16/3, 6/7

√5 is anirrational number since it is a surd and also it is no the square of one integerwith itself. √25 is a rational number due to the fact that it is a square that an creature 5with itself. 5/4 (1.25) is likewise a rational number. The is a end decimalbecause it has actually the finite number of digits ~ the decimal point. 6/5 (1.2)is likewise a reasonable decimal due to the fact that it has additionally the finite number of digitsafter the decimal point.

√36 is alsoa rational number since it is a perfect square. √8 is an irrational numberbecause that is a surd. The price of the fraction 16/3 is 5.33333… It method thatit is a repeating decimal. Together we recognize that repeating decimal is likewise a rationalnumber. The answer of the fraction 6/7 is 0.85714… It way that it is anon-repeating decimal and we have actually learned that all the non-repeating decimalsare irrational numbers.


In the end,we can plainly understand the difference between rational and also irrationalnumbers v the assist of these crucial points:

·Rationalnumbers = Perfect squares + Terminating decimals + Repeating decimals

·Irrationalnumbers = Surds + Non-repeating decimals

You justneed come take summary of a number. If the is a perfect square, terminatingdecimal or repeating decimal, it way that the a rational number. Top top the otherhand, if the is a surd or non-repeating decimal, it way that the is anirrational number.