Question

Express 0.136 as a rational no in the form of p/q
Note in 36 is a recurring decimal so there is a bar on top
Pls help fast

Answer 1

Given: The number 0.136(bar)

To find: Express 0.136 as a rational no in the form of p/q

Solution:

• Now we have given the number 0.136 (bar).

• Let it be x, so x = 0.136 (bar)

• We can rewrite it as : x = 0.136136136136...        ............(i)

• Now multiplying it with 1000, we get:

                 1000x = 136.136136136......                        ............(ii)

• Now applying, (ii) - (i), we get:

                 999x = 136

                 x = 136 / 999

Answer:

         So 136 bar can be written as 136 / 999 in  rational number.

Answer 2

Answer:

0.136 bar = $\frac{135}{990}$

Step-by-step explanation:

Let  x = 0.136 bar ---------> (1)

Multiply Eq. (1) by 10

=> 10x  =  1.36 bar

=> 10x  =  1.36363636..... ----------> (2)

Multiply Eq. (2) by 100

=> 1000x  =  136.36363636..... ---------> (3)

Subtract Eq. (2) from Eq. (3) :  [(3) - (2)]

  1000x  =  136.363636.....

 (-) 10x    = (-)   1.363636.....

    990x  =  135.000000.....

=> 990x  =  135

=>         x  =  $\frac{135}{990}$

Therefore 0.136 bar can be written as $\frac{135}{990}$ in p/q form.

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