Decimal Expansion of Rational and Irrational Numbers
Without actua...
Question
Without actual division , show that the following rational number is non-terminating repeating decimal : 64455
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Solution
Given rational number is 64455 Prime factorization of the denominator of the given rational number is
455=5×7×13
If the prime factorization of the denominator of any rational number is of the form 2m×5n where m and n are non-negative integers, then the decimal expansion of the given number is terminating else non-terminating repeating
(5×7×13) is not of the form (2m×5n) Hence given fraction has non -terminating repeating decimal expansion.