What is the 4000th digit following the decimal point in the expansion of 1/176?

Guest Apr 17, 2022

#1**+1 **

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".**

Guest Apr 17, 2022

#2**0 **

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**.

MaxWong Apr 17, 2022