Question

If $x=0.\overline{17}$, then which of the following statements are true?

(i) $100x=17.\overline{17}$
(ii) $100x-x=16.\overline{17}$
(iii) $99x=17$

• A. (i), (ii) and (iii)
• B. (i) and (iii)
• C. (i) and (ii)
• D. (i) only

Answer 1

The correct option is B (i) and (iii)

$x=0.\overline{17}$ ....(I)

Here the periodicity of the decimal is two.
So multiply both sides of (i) by 100 to get
$100x=17.\overline{17}$ ….(II)

Subtracting (I) from (II), we get

$99x=17$

Hence, the correct combination is (i) and (iii).