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.

BRAlNBOLT Jul 18, 2024

#1**+1 **

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! :)

NotThatSmart Jul 18, 2024