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9th Class Mathematics Number System and its Operations Question Bank Number System

  • question_answer
    \[\mathbf{1}.\mathbf{272727}=\mathbf{1}.\overline{\mathbf{27}}\]can be expressed in the form \[\frac{p}{q}\], where p and q are integers an\[\mathbf{q}\ne 0\] than it is equal to

    A)  \[\frac{106}{99}\]                    

    B)  \[\frac{127}{99}\]           

    C)  \[\frac{14}{11}\]   

    D)  \[\frac{27}{99}\]

    Correct Answer: C

    Solution :

    (c): Let \[x=1.\overline{27}\] then \[x=1.27272727\]?.(i) \[\Rightarrow 100x=127.272727\]   ????.(ii) On subtraction (i) and (ii) we get \[99x=\left( 127.272727... \right)-\left( 1.272727 \right)\] \[\Rightarrow 99x=126\] \[x=\frac{126}{99}=\frac{14}{11}\] Hence, \[1.\overline{27}=\frac{14}{11}\]                        


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