10th Class Mathematics Real Numbers Question Bank Real Numbers

  • 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)

    Correct Answer: C

    Solution :

    (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 \[\Rightarrow \]            \[9x=2.2\,\,\Rightarrow x=\frac{22}{90}=\frac{11}{45}\]


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