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10th Class Mathematics Real Numbers Question Bank MCQs - Real Number

  • question_answer
    The rational form of \[0.2\overline{54}\]is in the form of \[\frac{p}{q}\], then \[\left( p+q \right)\]is equal to 69.

    A) True

    B) False

    C) Can't say

    D) Partially True/False

    Correct Answer: A

    Solution :

    Let \[x=0.2\overline{54}\]. Then
    x =0.2545454...                         ...(i)
    On multiplying Eq. (i) by 100, we get
    \[\therefore \,\,\,100x=25.4545\]....                       ..(ii)
    On subtracting Eq. (i) from Eq. (ii),
    we get
                \[99x=25.2\]
     \[\Rightarrow x=\frac{252}{990}=\frac{14}{55}\]
     On comparing with \[\frac{p}{q}\], we get
    p = 14 and q = 55
    \[\therefore p+q=14+55=69\]
     


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