Question

Is it correct or wrong?

Answer 1

`\sf x = (23)/(90)`

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 = (23)/(90)}`

Answer 2

23/90

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.