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

Stanry Jun 24, 2024

#1**+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! :)

NotThatSmart Jun 24, 2024

#1**+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