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    When 0.434343..... is converted into a fraction, then the result will be :
    Question

    When 0.434343..... is converted into a fraction, then the result will be :

    A.

    43100\frac{43}{100}​​

    B.

    4.30.1\frac{4.3}{0.1}​​

    C.

    439.9\frac{43}{9.9}​​

    D.

    4399\frac{43}{99}​​

    Correct option is D

    Given:

    Repeating decimal = 0.434343...

    Solution:
    Let x = 0.430.\overline{43}​​
    Then multiplying both sides by 100 (since 2 digits repeat):

    100x = 43.4343.\overline{43}​​

    Now subtracting:

    100xx=43.430.43 99x=43 x=4399100x - x = 43.\overline{43} - 0.\overline{43} \\ \ \\ 99x = 43 \\ \ \\ x = \frac{43}{99}​​

    0.434343...=43990.434343... = \frac{43}{99}​​

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