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    Express 0.13241‾0.13\overline{241}0.13241​ in the form pq\frac{p}qqp​​ , where p and q are integers and q≠0.
    Question

    Express 0.132410.13\overline{241}​ in the form pq\frac{p}q​ , where p and q are integers and q≠0.

    A.

    333724160\frac{3337}{24160}​​

    B.

    380724975\frac{3807}{24975}​​

    C.

    328721780\frac{3287}{21780}​​

    D.

    330724975\frac{3307}{24975}​​

    Correct option is D

    Given:

    0.132410.13\overline{241}

    Solution:

    x = 0.132410.13\overline{241} ........ (1)

    ​​This means: 

    x = 0.132412412412…

    Multiply by 100 to shift the decimal point:

    100x = 13.241241 ......... (2)

    Multiply  (eq) 2 by 1000 

    100000x = 13241.241241....... (3)

    Subtract  equations (2) by (eq) 3 , we get

    99900x = 13228

    x=1322899900x= \frac{13228}{99900}

    x = 330724975\frac{3307}{24975}

    ​​The fraction form of 0.132410.13\overline{241} is :

    x = 330724975\frac{3307}{24975}​​

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