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Q.

The maximum number of digits be in the repeating block of digits in the decimal expansion of $117$ is ____.

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Detailed Solution

The maximum number of digits be in the repeating block of digits in the decimal expansion of

117

is 16.
Given number is

117

.
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

117

:

117 = 0 . 0588235294117647 ¯

Here is the process of long division of

117

:

Question Image

Thus

117 = 0 . 0588235294117647 ¯

Hence, the maximum number of digits in the repeating block of digits in the decimal expansion of

117

is 16.

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