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Q.


The maximum number of digits be in the repeating block of digits in the decimal expansion of 1 17  is ____.

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Detailed Solution

 The maximum number of digits be in the repeating block of digits in the decimal expansion of 1 17  is 16.
Given number is 1 17  .
Decimal expansion of Rational numbers: On dividing p by q, if the remainder becomes zero then the decimal expansion is terminating and if the remainder never becomes zero and Set of digits repeats periodically then the decimal expansion is non terminating repeating. It is also known as non terminating recurring decimal expansion.
Division of 1 17  :
1 17   = 0. 0588235294117647 ¯  
Here is the process of long division of 1 17   :
Question Image Thus 1 17   = 0. 0588235294117647 ¯  
Hence, the maximum number of digits in the repeating block of digits in the decimal expansion of 1 17   is 16.
 
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