Write a repeating decimal that is between 9/7 and 10/7. Justify your answer.

Question

Write a repeating decimal that is between 9/7
and 10/7.
Justify your answer.

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Xavia 5 months 2021-09-05T07:59:34+00:00 1 Answers 0 views 0

Answers ( )

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    2021-09-05T08:01:28+00:00

    Given:

    Two numbers are \dfrac{9}{7}  and \dfrac{10}{7}.

    To find:

    A repeating decimal that is between \dfrac{9}{7}  and \dfrac{10}{7}.

    Solution:

    Using calculator, we get

    \dfrac{9}{7}=1.285714285714...

    \dfrac{9}{7}=1.\overline{285714}

    and,

    \dfrac{10}{7}=1.42857142857 1...

    \dfrac{10}{7}=1.\overline{428571}

    Now, the repeating decimal that is between \dfrac{9}{7}  and \dfrac{10}{7} be x. So,

    1.\overline{285714}<x<1.\overline{428571}

    On analyzing the numbers to hundredth places, we get 1.28 < 1.33 < 1.42, therefore

    1.\overline{285714}<1.3333...<1.\overline{428571}

    1.\overline{285714}<1.\overline{3}<1.\overline{428571}

    And we know that 1.\overline{3} is the decimal form of \dfrac{4}{3}.

    Therefore, the required number is 1.\overline{3} .

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