Answer: To find the decimal expansion of 5/7, we can perform long division as follows:
0.7│5.0
4 2
────
8 │ 30
28
───
20 │ 200
196
────
4
Hence, 5/7 = 0.714285... where the digits 714285 repeat indefinitely. To find the maximum number of digits in the repeating block of digits, we can observe that the repeating block will be at most 6 digits long because 7 has a factor of 2 and 5, and therefore 7 divides 10^6 - 1 = 999999.
In fact, we can see that the repeating block in this case has 6 digits, since the digits 714285 repeat indefinitely, and there are 6 digits in this repeating block. Therefore, the maximum number of digits in the repeating block of digits in the decimal expansion of 5/7 is 6.
Explanation: