In the decimal representation of rac{1}{7}, the 100th digit to the right of the decimal is?
Solution
The digits to the right of the decimal place in the decimal representation of rac{1}{7} occur in blocks of 6, repeating the block of digits 142857. Since , then the 96th digit to the right of the decimal place is the last in one of these blocks; that is, the 96th digit is 7. This means that the 97th digit is 1, the 98th digit is 4, the 99th digit is 2, and the 100th digit is 8.
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