Question

If $x=0.\overline{29}$, then which of the following statements are true?

(i) $100x=29.\overline{29}$
(ii) $100x-x=28.\overline{29}$
(iii) $99x=29$

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

Answer 1

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

$x=0.\overline{29}$ ....(1)

Here the periodicity of the decimal is two.
So, multiply both sides of (1) by 100 to get
$100x=29.\overline{29}$ ….(2)

Subtracting (1) from (2), we get
$99x=29$

Hence, the correct statements are (i) and (iii).