Question

Find two rational numbers between 0.121221222122221... and
0.141441444144441... in the form p/q, where p and q are integers and q ≠ 0.

Answer 1

Step-by-step explanation:

Given :

0.121221222122221... and

0.141441444144441...

To find: Find two rational numbers between 0.121221222122221... and

0.141441444144441... in the form p/q, where p and q are integers and q ≠ 0.

Solution:

Given numbers are irrational number because both numbers 0.121221222122221... and

0.141441444144441... are non-terminating and non-repeating.

Step 1: There are infinite rational numbers between these two irrational numbers.I am writing two here

1) 0.131313...

2) 0.132132132...

Step 2: Writing p/q form of 0.131313...

Let

$x = 0.131313...eq1 \\ \\ 100x = 13.131313...eq2$

subtract eq2-eq1

$99x = 13 \\ \\ x = \frac{13}{99}$

Step 3: To write 0.132132132... in p/q

Let

$x = 0.132132132...eq3 \\ \\ 1000x = 132.132132132...eq4$

subtract eq4-eq3

$999x = 132 \\ \\ x = \frac{132}{999}$

Thus,

Two rational numbers between given irrational numbers may be 13/99 and 132/999.

Final answer:

Two rational numbers may be

$\bold{\frac{13}{99}} \\ \\ \bold{\frac{132}{999}}$

Hope it helps you.

Note*: Answer may be different in book,as there are infinite rational numbers possible.

To learn more on brainly:

1) visualise 2.3567 on the number line . upto

three decimal places, using successive magnification.

https://brainly.in/question/41094222

2) Express each of the following as vulgar fraction: 0.263(bar on 63)

please answer it fast

https://brainly.in/question/40700751

Answer 2

Given :  

0.121221222122221... and 0.141441444144441

To Find :  two rational numbers between in the form p/q, where p and q are integers and q ≠ 0

Solution:

0.121221222122221... and 0.141441444144441

number starting with 0.13  will be in between  0.121221222122221... and 0.141441444144441

Lets take  few numbers

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  

There always exist infinite rational number between any two distinct real number

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