Answer:
5
Step-by-step explanation:
Lets meassure with f(x) the value of the x_th decimal. Lets calculate f(100) slowly.
For x in {1,...,9}, f(x) = x
Now, all following values should take 2 decimal places until we reach 100. So the 100th must belong to one of those numbers. 9 is the 9th decimal, and if we advance 10 numbers, we will move 20 places and we will obtain that 9 is the 29th decimal, followed by 2 (the start of 20). Furthermore, by moving 20 places, we will get that 9 is also the 49th decimal, followed by 3. 9 is the 69th decimal, followed by 4, and 9 is the 89th decimal. Hence
- f(90) = 5 (start of 50)
- f(91) = 0 (end of 50)
- f(92) = 5
- f(93) = 1
- f(94) = 5
- f(95) = 2
- f(96) = 5
- f(97) = 3
- f(98) = 5
- f(99) = 4
- f(100)= 5
The 100th digit is 5
