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Friday, 20 October 2017

Difference Between Rational and Irrational Numbers

Difference Between Rational and Irrational Numbers

Definition of the Rational numbers

what is the difference between rational and irrational numbers
Rational vs Irrational numbers

In Mathematics, rational numbers are those numbers which are written in the form of p/q such that q≠0.  The condition for the rational numbers is that both p and q should belong to Z and Z is a set of integers. The simplest examples of the rational numbers are given below;     
a)     1/9    
b)     10  or 10/1

Definition of irrational numbers

The irrational numbers are those numbers which are not written in the form of the p/q. The simplest examples of the irrational numbers are given below;
         a)     √3
         b)      3/0

Difference between rational and irrational numbers

Most of the students are not able to know the difference between the rational and irrational numbers just with the help of their definitions. They require more detail to find the difference between rational and irrational numbers. The key difference between them can be explained in the following way;
     1)      All the perfect squares are the rational numbers and the perfect squares are those numbers which are easily simplified to remove the square roots. The examples of the perfect squares are √ 4, √ 49, √ 324, √ 1089  and √ 1369.
On the other hands, all the Surds are the irrational numbers and the Surds are those numbers which can’t be simplified to remove the square root. The examples of the Surds are √2, √3 and √7.

        2)     All the repeating decimals are the rational numbers and the repeating decimals are those decimals whose digits repeat over and over again without end. The examples of the repeating decimals are .33333333, .222222 and .555555.
    On the other hand, all the non-repeating decimals are the irrational numbers and the non-repeating numbers are those digits which don’t repeat over and over again. The examples of the non-repeating decimals are .0435623, .3426452 and .908612.

      3)    The numbers which are written without denominators are rational numbers. The examples of these kinds of numbers are 8 and 9. These numbers are written in the form of p/q as 8/1 and 9/1.
    The numbers whose denominators are 0 are called the irrational numbers like 8/0 and 9/0.

     4)    0.5 is called the rational number because it can be written in the form of p/q like 5/10.

     5)     Pi is the irrational number. Its reason is that it gives us the non-repeating decimal 3.14159……

     6) From the above discussion, we can conclude that the rational numbers are expressed in the decimal as well as in the fraction form. On the other hand, if we talk about the irrational numbers, then we come to know that the irrational numbers are expressed in the decimal form only.

     7) A set of rational numbers is represented by "R". On the other hand, a set of irrational numbers is represented by R'. If we take the union of the R and R', then we will get a set of the real numbers. The set of the real numbers is represented by "Z".  In Mathematical form, we can write it as;

      R U R' = Z

    This is the basic difference between the rational and irrational numbers. 

    You can also read our other interesting posts like "Why is Milk White?" and "Difference between mass and weight".





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