+892 Find the $4000$th digit following the decimal point in the expansion of $\frac{1}{17}$.
Be sure to include complete explanations with your answer, using complete sentences. Imagine you were going to show your solution to a classmate, and try to write your solution so that they could understand it without doing any extra work.
+1837 First, let's note that 1/17 is a repeating decimal.
We have that \(1/17 = 0.\overline{0588235294117647}\)
There are 16 repeating digits.
Thus, we do 4000/16. We get
\(4000/16=250\)
Since it's divisible, it means the last digit of the repeating part is our answer, which is 7.
So 7 is our answer.
Thanks! :)
