# RATIONAL NUMBERS BETWEEN 1 AND 2

## About "Rational numbers between 1 and 2"

Rational numbers between 1 and 2 :

We can find many rational numbers between 1 & 2 using the formula method.

## Formula method

Let ‘a’ and ‘b’ be any two given rational numbers. We can find many rational numbers q1, q2, q3,...in between a and b as follows :

The numbers q2, q3 lie to the left of q1. Similarly, q4, q5 are the rational numbers between ‘a’ and ‘b’ lie to the right of q1 as follows:

Important note :

Average of two numbers always lies between them.

## Rational numbers between 1 and 2

Now, let us find rational numbers between 1 & 2

Solution :

Let a = 1 and b = 2

Let q1, q2, q3, q4, q5,.......... be the rational number between 3 and 4.

Then, we have

q1  =  1/2 x (a + b)

q1  =  1/2 x (1 + 2)

q1  =  1/2 x (3)

q1  =  3/2

Let q2 be the rational number between 1 and 3/2

Then, we have

q2  =  1/2 x (1 + 3/2)

q2  =  1/2 x 5/2

q2  =  5/4

Let q3 be the rational number between 1 and 5/4

Then, we have

q3  =  1/2 x (1 + 5/4)

q3  =  1/2 x 9/4

q3  =  9/8

Let q4 be the rational number between 1 and 9/8

Then, we have

q4  =  1/2 x (1 + 9/8)

q4  =  1/2 x 17/8

q4  =  17/16

Let q5 be the rational number between 1 and 17/16

Then, we have

q5  =  1/2 x (1 + 17/16)

q5  =  1/2 x 33/16

q5  =  33/32

Let q6 be the rational number between 1 and 33/32

Then, we have

q6  =  1/2 x (1 + 33/32)

q6  =  1/2 x 65/32

q6  =  65/64

In this way, we can find many rational numbers between 1 & 2 as given below.

1 < 65/64 < 33/32 < 17/16 < 9/8 < 5/4 < 3/2 < 2

After having gone through the stuff given above, we hope that the students would have understood "Rational numbers between two rational numbers".

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