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10th Class Mathematics Real Numbers Question Bank Real Numbers

  • question_answer
    A real number \[\frac{{{2}^{2}}\times {{3}^{2}}\times {{7}^{3}}}{{{2}^{2}}\times {{5}^{3}}\times {{3}^{5}}\times {{7}^{4}}}\]will have     _______.

    A) Terminating decimal expansion         

    B) Non-terminating decimal expansion     

    C)  Repeating decimal expansion

    D)  Both (b) and (c)        

    Correct Answer: D

    Solution :

    Given number, \[\frac{{{2}^{2}}\times {{3}^{2}}\times {{7}^{3}}}{{{2}^{2}}\times {{5}^{3}}\times {{3}^{5}}\times {{7}^{4}}}=\frac{1}{{{3}^{3}}\times {{5}^{3}}\times 7}\] If the prime factorization of denominator has power of 2, power of 5 or both, then the number should always be terminating decimals So, it is a non-terminating and repeating decimal expansion.         


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