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Question:

What can be the maximum number of digits in the repeating block of digits in the decimal expansion of 1/17?

Solution:

When1is divided by17, we get,117=0.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯0588235294117647So, the number of digit in the repeating block of digit in the decimal expansion of117=16