without long division method ,state wether 935/10500 will have the terminating or non terminating or repeating decimal expantion​

Question

without long division method ,state wether 935/10500 will have the terminating or non terminating or repeating decimal expantion​

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Valentina 1 week 2021-09-13T09:11:23+00:00 2 Answers 0 views 0

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    0
    2021-09-13T09:12:27+00:00

    Answer:

    Non – terminating

    Step-by-step explanation:

    935/10500

    -> 935 /10500= 187 / 2250

    -> 187 / (5)3 *(3)2* 2

    so , it can’t be divide properly

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    0
    2021-09-13T09:13:16+00:00

    Step-by-step explanation:

    Given that:935/10500

    To check:

    without long division method, find the number have the terminating or non terminating or repeating decimal expansion

    Solution: Check for any common factor in numerator and denominator(Number should be simple rational number)

    After inspection it is clear that,5 is common in both,cancel that

     \frac{935}{10500}  \\  \\  =  \frac{187}{2100}  \\  \\

    2) Do prime factors of denominator,if they are in the form of

     {2}^{n}  \times  {5}^{m}  \: m ,\: n \:  belongs \: to \: positive \: integer \\

    then given number have terminating decimal expansion otherwise non-terminating repeating decimal expansion

    So,

     \frac{187}{2100}  \\  \\  =  \frac{187}{ {2}^{2} \times 3 \times  {5}^{2} \times 7  }  \\  \\

    Here we can easily see that

    {2}^{2} \times 3 \times  {5}^{2} \times 7 \: \not =  {2}^{n}  \times  {5}^{m}  \\  \\

    So,given rational number(935/10500) is non-terminating repeating decimal expansion.

    Hope it helps you.

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