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The rational number 441/(2^ 5 x5^ 7x7^2) a terminating or a non-terminating decimal representation?
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The rational number 441/(2^ 5 x5^ 7x7^2) a terminating or a non-termin...
Terminating or Non-Terminating Decimal Representation of 441/(2^5 x5^7x7^2)



  • Definition of Terminating and Non-Terminating Decimal Representation:


    • A terminating decimal representation is a decimal representation of a rational number that ends after a finite number of digits.

    • A non-terminating decimal representation is a decimal representation of a rational number that continues on infinitely without repeating.





  • Simplifying the Rational Number:


    • 441 = 3^2 x 7^2

    • 2^5 = 32

    • 5^7 = 78125

    • 7^2 = 49

    • 441/(2^5 x 5^7 x 7^2) = (3^2 x 7^2) / (2^5 x 5^7 x 7^2)

    • 441/(2^5 x 5^7 x 7^2) = (3^2)/(2^5 x 5^7) = 9/781250





  • Determining if the Decimal Representation is Terminating or Non-Terminating:


    • To determine if the decimal representation of 9/781250 is terminating or non-terminating, we can convert the fraction to a decimal.

    • To do this, we can divide 9 by 781250 using long division.

    • After performing long division, we find that the decimal representation of 9/781250 is 0.000011520.

    • Since the decimal representation of 9/781250 ends after a finite number of digits, it is a terminating decimal representation.




Conclusion:

The rational number 441/(2^5 x 5^7 x 7^2) can be simplified to 9/781250 and its decimal representation is a terminating decimal representation.
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The rational number 441/(2^ 5 x5^ 7x7^2) a terminating or a non-terminating decimal representation?
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