Question

is it correct or wrong?

Answer 1

Answer:

23/90

Step-by-step explanation:

It's incorrect.

You started out correctly. You need to subtract the equations, not add them. By subtracting the equations, you get rid of the repeating part.

x = 0.2555...

      100x = 25.555...

(-)       10x =  2.5555         <----------   Up to here you were correct, but

--------------------------------                    you need to subtract the equations

         90x = 23

90x/90 = 23/90

x = 23/90

BTW, to check, just take a calculator and divide 23 by 90. If you don't get 0.2555..., then you know it's incorrect.

Answer 2

Answer:

$\sf x = \dfrac{23}{90}$

Step-by-step explanation:

Writing a rational number in p/q form:

   x = 0.25555....  -------------(i)

Now multiply equation (i) by 100,

   100x = 25.5555...  ---------(ii)

Again multiply equation (i) by 10,

     10x = 2.5555.... -----------(iii)

Now, subtract (iii) from (ii),

        100x = 25.555....

           10x =   2.555.....

        -              -                 {Subtract}

           90x = 23

                $\sf \boxed{x = \dfrac{23}{90}}$