Question

How can one tell a rational and irrational number apart?

Answer 1

Hint:We know that the basic definition of a rational number is: Numbers which are positive or negative and that can be expressed in the form $\dfrac{p}{q}$ where $q \ne 0$. Also irrational numbers are numbers which cannot be expressed in the form $\dfrac{p}{q}$ where$q \ne 0$.So by using the basic definitions we can solve the question which is to tell rational and irrational numbers apart.

Complete step by step answer:
Given, \[{\text{Rational and irrational numbers}}...............................\left( i \right)\].
Now we know that Rational numbers are numbers which are positive or negative and that can be expressed in the form $\dfrac{p}{q}$ where $q \ne 0$. Also irrational numbers are numbers which cannot be expressed in the form $\dfrac{p}{q}$ where $q \ne 0$. So these two are quite opposite to each other. Now let’s find the differences between rational and irrational numbers by which we can tell apart them:

Rational numbers	Irrational numbers
Rational numbers can be expressed as fractions of whole numbers.When we write the result of a fraction of a rational number the decimal either stops after some digit or it repeats with a certain pattern.E.g.$\dfrac{2}{3} = 0.6666666..................$	We cannot express irrational numbers as fractions or as a ratio of two whole numbers.An irrational number first of all cannot be written as a fraction, also while writing the decimal number it goes on and on without any pattern.E.g.$\sqrt 2 = 1.414213$

Now from the above mentioned points we can easily tell apart a rational and irrational number.
Note:Surds are a type of irrational number that cannot be represented as a fraction of whole numbers or also as a decimal of recurring digits. Also if we want to represent an irrational number as a rational number there are many methods present and the process of converting an irrational number to a rational number is called rationalization.