+0  
 
-1
1
2
avatar+1335 

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

 Jun 16, 2024
 #1
avatar+1075 
+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! :)

 Jun 16, 2024
 #2
avatar+1075 
+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! :)

 Jun 17, 2024

1 Online Users

avatar