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    Convert 0.236‾0.2\overline{36}0.236​  into a regular fraction.
    Question

    Convert 0.2360.2\overline{36}​  into a regular fraction.

    A.

    733\frac{7}{33}​​

    B.

    944\frac{9}{44}​​

    C.

    1766\frac{17}{66}​​

    D.

    1355\frac{13}{55}​​

    Correct option is D

    ​​Given:
    Recurring decimal 0.23636...

    Solution:

    Let X = Multiply X by 10

    10X = 2.36......  (1)

    1000X = 236.36.... (2)

    Subtract (2) from  (1)

    1000X - 10X = 236.36... - 2.36...

    990X = 234

    X = 234990\frac {234}{990}​​

    X = 1355\frac {13}{55}​​

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