• # question_answer Match the following. Column-l Column-II (P) Rational form of $0.\overline{32}$is (i)   $\frac{14}{55}$ (Q) Rational form of $0.\overline{254}$is (ii)  $\frac{11}{45}$ (R) Rational form of $0.\overline{12}$is (iii)  $\frac{32}{99}$ (S) Rational form of $0.\overline{24}$is (iv)  $\frac{11}{90}$ A) (P)$\to$(iii);(Q)$\to$(iv);(R)$\to$(i);(S)$\to$(ii)B) (P)$\to$(iv);(Q)$\to$(i);(R)$\to$(ii);(S)$\to$(iii)C) (P)$\to$(iii);(Q)$\to$(i);(R) $\to$(iv);(S)$\to$(ii)D)  (P)$\to$(i);(Q)$\to$(iii);(R)$\to$(iv);(S)$\to$(ii)

(P) Let $x=0.\overline{32}$ $\Rightarrow$            $x=0.3232332.......$         ?..(1) $\Rightarrow$            $100x=32.3232.....$         ?..(2) Subtracting (1) from (2), we get                         $99x=32\Rightarrow x=\frac{32}{99}$             (Q) Let $x=0.2\overline{54}$             $\Rightarrow$            $x=0.25454.....$                 ?..(1)             $\Rightarrow$            $100x=25.45454.....$         ??(2)             Subtracting (1) from (2), we get             $99x=25.2\,\Rightarrow x=\frac{252}{990}=\frac{14}{55}$             (R) Let  $x=0.1\overline{2}$             $\Rightarrow$            $x=0.1222....$                                    ?.(1)             $\Rightarrow$            $10x=1.222.....$                     ?.(2)             Subtracting (1) from (2), we get $\Rightarrow$            $9x=2.2\,\,\Rightarrow x=\frac{22}{90}=\frac{11}{45}$