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What digit is there? (Posted on 2021-11-15) Difficulty: 2 of 5
In the digital expansion of 5/21 what digit is located at the 521st place to the right of the decimal point?

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution Full Solution Comment 2 of 2 |
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

  Posted by K Sengupta on 2021-11-16 01:29:37
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