Answer
Verified
414.3k+ views
Hint: Try to recall the definition of rational and irrational numbers. We can also pick any two random rational numbers and one random irrational number that is greater than 0.5 and less than 0.6.
Complete step-by-step solution -
Before moving to the options, let us talk about the definitions of rational numbers followed by irrational numbers.
So, rational numbers are those real numbers that can be written in the form of $\dfrac{p}{q}$ such that both p and q are integers and $q\ne 0$ . In other words, we can say that the numbers which are either terminating or recurring when converted to decimal form are called rational numbers. All the integers fall under this category.
Now, moving to irrational numbers.
Those real numbers which are non-terminating and non-recurring are termed as irrational numbers.
The roots of the numbers which are not perfect squares fall under the category of irrational numbers. $\pi \text{ and }e$ are also the standard examples of irrational numbers.
Now moving to the solution. First, let us find two rational numbers, which are greater than 0.5 and less than 0.6. The two rational numbers can be 0.55 and 0.56. Next, let us think of an irrational number, which lies between 0.5 and 0.6. So the irrational number can be $\dfrac{1}{\sqrt{3}}$ , whose approximate value is about 0.5773.
Note: We should also remember that there exist infinite rational as well as irrational numbers lying between two distinct rational numbers. Here we need to remember the definition of rational and irrational numbers. 0.55 and 0.56 can be written as $\dfrac{p}{q}$ where $q\ne 0$.
Complete step-by-step solution -
Before moving to the options, let us talk about the definitions of rational numbers followed by irrational numbers.
So, rational numbers are those real numbers that can be written in the form of $\dfrac{p}{q}$ such that both p and q are integers and $q\ne 0$ . In other words, we can say that the numbers which are either terminating or recurring when converted to decimal form are called rational numbers. All the integers fall under this category.
Now, moving to irrational numbers.
Those real numbers which are non-terminating and non-recurring are termed as irrational numbers.
The roots of the numbers which are not perfect squares fall under the category of irrational numbers. $\pi \text{ and }e$ are also the standard examples of irrational numbers.
Now moving to the solution. First, let us find two rational numbers, which are greater than 0.5 and less than 0.6. The two rational numbers can be 0.55 and 0.56. Next, let us think of an irrational number, which lies between 0.5 and 0.6. So the irrational number can be $\dfrac{1}{\sqrt{3}}$ , whose approximate value is about 0.5773.
Note: We should also remember that there exist infinite rational as well as irrational numbers lying between two distinct rational numbers. Here we need to remember the definition of rational and irrational numbers. 0.55 and 0.56 can be written as $\dfrac{p}{q}$ where $q\ne 0$.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Write an application to the principal requesting five class 10 english CBSE
Difference Between Plant Cell and Animal Cell
a Tabulate the differences in the characteristics of class 12 chemistry CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
Discuss what these phrases mean to you A a yellow wood class 9 english CBSE
List some examples of Rabi and Kharif crops class 8 biology CBSE