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Question: If \(\frac{n}{7}\), n ÎN is a non-terminating and is a recurring decimal rational number. After deci...

If n7\frac{n}{7}, n ÎN is a non-terminating and is a recurring decimal rational number. After decimal at some stage, digits start repeating in groups continuously. If smallest such group has r digits, then –

A

Maximum value of r is 3

B

Maximum value of r is 7

C

Maximum value of r is 6

D

Maximum value of r is 9

Answer

Maximum value of r is 6

Explanation

Solution

17\frac{1}{7} = 0.142857‾0.\overline{142857}

17\frac{1}{7} = 0.142857142857

Clearly these are 6 digits in repeating group

A repeating group can not contain 7 or more than 7 digits because the divisor is 7.

Hence maximum value of r is 6.