Finding Rational Numbers between two Rational Numbers


 
 
Concept Explanation
 

Finding Rational Numbers Between Two Rational Numbers

Finding Rational Numbers between two Rational Numbers:

There are infinitely many rational numbers between any two rational numbers.

To find rational numbers between two rational numbers there can be different cases

Case I:To find rational Number between the numbers having no denominator

We know that between two rational numbers x and y such that x < y there us a rational number large frac{x+y}{2}. That is, large x<frac{x+y}{2}<y

In this case we will follow the following steps:

Step 1: First find the mid number between the two given numbers.

Step 2: Find the mid number between the first given number and the mid number found in step 1.

Step 3: Find the mid number between the second given  number and the mid number found in step 1.

Step 4: Repeat the step 2 and 3 for the mid numbers found in step 2 and step 3.

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Sample Questions
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Question : 1

How many rational number exists between any two distinct rational numbers ?

Right Option : D
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Question : 2

The number of rational numbers between large sqrt{3 };;and ;;sqrt{5} is ________________

Right Option : D
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Explanation
Question : 3

Between 3 and 4 there are 

Right Option : D
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Explanation
 
 


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