In the digital expansion of 5/21 what digit is located at the 521st place to the right of the decimal point?
The digital expansion of 5/7 is well known, and it is:
0.7142857714285.......(the string 714285 repeats indefinitely).
Dividing by 3, we have the digital expansion of 5/21 as:
0.238095238095.......(the string 238095 repeats indefinitely)
The above string has length 6.
Now, 521=6*86+5
Accordingly, the digit at the 521th place is the 5th member of the string 238095, which is 9.
Consequently, the required digit is 9
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