Question

Express 1.36363636........ In p/q form

Answer 1

hey mate!

✨here's your answer!✨

let x = 1.3636363636.....

so, 100x = 136.36363636...

=> 100x-x = 136.36 - 1.36

=> 99x = 135

=> x = 135/99 or 45/33

so, 1.36363636... in p/q form = 135/99 or 45/33.

$\bf{hope\: you\: understood!}$✌️

Answer 2

Answer:

1.363636..... =  $\frac{135}{99}$   or

1.363636..... =  $\frac{15}{11}$

Step-by-step explanation:

Given 1.363636... is a non-terminating recurring decimal expansion. We need to convert it into p/q form where p and q are integers and q≠0.

Let us call 1.363636.... as '$x$'

       $x = 1.363636....$

As there are two numbers repeating, multiply $x$ by 100,

      $100x = 100 \times 1.363636...$

      $100x = 136.3636....$

Now, write 136.3636..... in the form $x$ + some number

      $100x = 1.3636.... + 135$

      $100x=x+135$

      $100x-x = 135$

      $99x = 135$

      $x = \frac{135}{99} = \frac{45}{33} = \frac{15}{11}$

i.e., $1.363636..... = \frac{15}{11}$

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