What is the 4000th digit following the decimal point in the expansion of 1/176?
1/176 ==0.00568181818181.............etc.
It has a "period" of 2.
Therefore: 4000 mod 2==0, which means it should be the 2nd repeating digit, which is "1".
+9674 We can actually divide 1 by 176 and see the result.
\(\dfrac1{176} = 0.0056818181\dots= 0.0056\overline{81}\)
Therefore, starting from the 5th digit following the decimal point,
\(\text{The }N\text{-th digit following the decimal point} = \begin{cases}8\text{, }N\text{ is odd}\\1, \text{ otherwise}\end{cases}\)
Therefore, the 4000th digit is 1.
