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

1 answer

To find the 4000th digit following the decimal point in the expansion of \frac{1}{17}, we can perform long division to calculate the decimal representation of \frac{1}{17}.

When performing long division, the decimal representation of \frac{1}{17} repeats after every 16 digits. Therefore, we can first find the remainder after dividing 1 by 17 and then continue to divide the remainder by 17 until we have found the 4000th digit following the decimal point.

1 รท 17 = 0.0588235294117647 (dividend = 1, remainder = 1)
0.0588235294117647

We see that the decimal representation of \frac{1}{17} repeats the block of digits 0588235294117647 after every 16 decimal places.

We can calculate that the digit in the 4000th position after the decimal point is 5.