What is the 489th digit in the number 123456789101112 ... ?
What is the 489th digit in the number 123456789101112 ... ?
0
3
6
9
Solution
Digits 1-9 (single-digit numbers) use $9$ digits. Two-digit numbers 10-99 contribute $90\times2 = 180$ digits, taking us to digit $9+180 = 189$. Remaining digits to reach 489: $489-189 = 300$. Three-digit numbers use 3 digits each; $300/3 = 100$ complete numbers, ending at the 100th three-digit number $100+100-1 = 199$. So digit 489 is the last digit of 199, which is 9.