Find the 4000th digit following the decimal point in the expansion of \frac{1}{17}.

ABJeIIy Jun 16, 2024

#1**+1 **

First, it's important to note that 1/17 is a repeating decimal. We have

\(1/17=0.\overline{0588235294117647}\)

Now, we must find which digit is the 4000th.

We have \(4000/17=235R5\)

So, our answer is the fifth digit in the 16 repeating digits.

The number we are looking for is 2.

So our final answer is 2.

Thanks! :)

NotThatSmart Jun 16, 2024

#2**+1 **

I made a slight mistake for this problem.

We have \(1/17=0.\overline{0588235294117647}\). There are 16 repeating digits in this decimal.

Thus, we must do \(4000/16=250\)

Since the number is divisble, the last digit is the 4000th digit.

So 7 is our answer.

Thanks! :)

NotThatSmart Jun 17, 2024