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2 ÷ 7 = 0.285714285714...

ie it repeats the 6 digits: {2, 8, 5, 7, 1, 4}.

Therefore taking the digit place modulus 6 will tell you which of these digits occupies that position (if the result of the modulus is 0, the 6th of the list, ie the '4', is the required digit).

1001 mod 6 = 5

→ 1001st digit of 2/7 is a '1' (assuming the 1st digit is the 1st digit after the decimal point).

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Q: What is the digit in the 1001st place when 2 is divided by 7?
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