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Answer :

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Answer:

13/100 ,  131/1000 , 33/250

Step-by-step explanation:

Question to Answer:

Two rational numbers between in the form p/q, where p and q are integers and q ≠ 0

Solve:

0.121221222122221 and 0.141441444144441

Thus, Number starting with 0.13  will be in between 0.121221222122221... and 0.141441444144441

Few Number Are:

0.13  , 0.131  , 0.132

= 13/100  ,  131/1000 ,  132/1000  

132/100   = 33/250

13/100 ,  131/1000 , 33/250 are few  rational numbers between   0.121221222122221... and 0.141441444144441  

Therefore, There always exist infinite rational number between any two distinct real number .

[CloudBreeze]

Step-by-step explanation:

Basically provided with two number 0.121221222122221 and 0.141441444144441 and asked to find the rational number between them in the form p/q where p and q are integers. (q ≠ 0).

First let's try to understand what rational number is! A rational number is a number which can be written in the form of fraction and denominator can't be zero. As already said in question; in the form p/q where q ≠ 0.

For instance:

→ 13/100 = 0.13 or 0.1313131313....

[ x = 0.131313...

[ 100x = 13.13131...

[ On subtracting we get 99x = 13, x = 13/99 ]

→ 131/1000 = 0.131

[ x = 0.1313131...

[ 1000x = 131.13131...

[ On subtracting we get 999x = 131, x = 131/999 ]

→ 132/1000 = 0.132

[ x = 0.132132...

[ 1000x = 132.132132...

[ On subtracting we get 999x = 132, x = 132/999 ]

Hence, 0.13, 0.131, 0.132 are some of the rational numbers between 0.121221222122221 and 0.141441444144441.

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