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