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Question 2

What is the 2019th digit to the right of the decimal point, in the decimal representation of $$\frac{5}{28}$$?

Solution

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Long division gives $$\frac{5}{28}=0.1\overline{785714}$$, with the first digit 1 followed by a repeating block of 6 digits starting from the second decimal place. Since $$(2019-2) \bmod 6 = 1$$, the 2019th digit matches the 2nd digit of the repeating block "785714", which is 8.

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