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    Express 4.142‾4.\overline{142}4.142​ in the form pq\frac{p}{q}qp​​, where p and q are integers and q≠0.
    Question

    Express 4.1424.\overline{142}​ in the form pq\frac{p}{q}​, where p and q are integers and q0.

    A.

    4142999\frac{4142}{999}​​

    B.

    4136999\frac{4136}{999}​​

    C.

    4140999\frac{4140}{999}​​

    D.

    4138999\frac{4138}{999}​​

    Correct option is D

    Given:

    Given number =4.1424.\overline{142}​​

    Solution:

    Let x = 4.142142…

    Then 1000x = 4142.142…

    1000x - x = 4142.142142… - 4.142142..

    999x = 4138

    x =4138999 \frac{4138}{999}​​

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