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.

Rangcr897 Jul 3, 2024

#2**+1 **

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! :)

NotThatSmart Jul 3, 2024