Question

represent o. 23555...... in p/q from​

Answer 1

Answer:

53/225

Step-by-step explanation:

0.23555... can be said as 0.235 bar{ on 5 }

 Let a = 0.235 bar

        Multiply both sides by 100 :

⇒ 100a = 100*0.235 bar

⇒ 100a = 23.5 bar    ...( 1 )

      Multiply both sides by 10:

⇒ 1000a = 235.5 bar   ...( 2 )

 

   Subtract ( 1 ) from ( 2 )

    1000a = 235.5 bar

    - 100a = - 23.5 bar

     900a =  212        

a = 212 / 900

    = 106 / 450

    = 53 / 225

Hence 53/225 = 0.23555...

Answer 2

Here , we are given the following recurring decimal expression , which we have to convert into a fraction of the form p / q where q is not equal to 0 and ( p, q ) = 1 .

Given -

$\sf{ 0.23555............ \infty }$

Solution -

Let us assume that this is equal to X .

So ,

$\sf{ X = 0.23555............ \infty }$

So , let us find the value of 10x

$\sf{ 100X = 23.555............ \infty } .......... [ 1 ]$

So , On Multiplying X with 1000 -

$\sf{ 1000x = 23.5555....... \infty } ............ [ 2 ]$

Now , let us Subtract Equation 1 from Equation 2

So ,

$\sf{ 1000x = 235.555....... \infty } ............ [ 2 ]$

$\sf{ 100X = 23.555............ \infty } ........ [ 1 ]$

$\sf{ \bold{ Subtracting \: - }}$

$\sf{ \bold{ LHS \: - } => 100x - 100x = 900x }$

$\sf{ \bold{ RHS \: - } => 235.555....... \infty - 23.555............ \infty = 212}$

So,

$\sf{ 900x = 212} \\ \\ \sf{ => x = \dfrac{ 212}{900} } \\ \\ \sf{ => x = \dfrac{ 53}{ 225 } } ....... [ A ]$