RATIONAL NUMBERS BETWEEN 1 AND 2

In this section, we will learn how to find rational numbers (a/b, b ≠ 0) between 1 and 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

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.