+0  
 
0
2
1
avatar+257 

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

 Jun 24, 2024

Best Answer 

 #1
avatar+1230 
+1

Let's note that 1/17 is a repeating decimal, which can make our lives quite easy!

We have

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

 

There are 16 repeating digits. Thus, we simplfy have

\(4000/16=250\)

 

Thus, the last digit, 7 is the 4000th digit. 

 

So our answer is 7. 

 

Thanks! :)

 Jun 24, 2024
 #1
avatar+1230 
+1
Best Answer

Let's note that 1/17 is a repeating decimal, which can make our lives quite easy!

We have

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

 

There are 16 repeating digits. Thus, we simplfy have

\(4000/16=250\)

 

Thus, the last digit, 7 is the 4000th digit. 

 

So our answer is 7. 

 

Thanks! :)

NotThatSmart Jun 24, 2024

2 Online Users