Questions & Answers

Question

Answers

Answer
Verified

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 $q\ne 0$.

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 $q\ne 0$.

×

Sorry!, This page is not available for now to bookmark.