+161 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.
+1786 Let's first take a look at the fraction 1/17.
It has 16 repeating digits in the form of \(0. \overline{0588235294117647}\)
We simplfy have to find which digit the 4000th lies on.
First, let's do 4000/16.
We get \(4000/16=250\)
So the 4000th digit is the last digit of the repeating decimal, which is 7.
So 7 is our answer.
Thanks! :)
