+0

# Decimals

0
83
2

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

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".

Apr 17, 2022
#2
+9459
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.

Apr 17, 2022