What is the 489th digit in the number 123456789101112...?

To find the 489th digit, we count the number of digits used by integers starting from 1. First, numbers 1 to 9 are single-digit numbers. This uses 9 digits. Remaining digits needed: 489 minus 9 equals 480 digits. Next, we look at two-digit numbers, which run from 10 to 99. There are 90 such numbers, using 180 digits. Since 480 is greater than 180, we exhaust all two-digit numbers. Remaining digits needed: 480 minus 180 equals 300 digits. Now we move to three-digit numbers, starting from 100. Each number uses 3 digits. To find how many three-digit numbers we need to cover 300 digits, we divide 300 by 3, which equals 100. The 100th three-digit number starting from 100 is 199. Because the division has no remainder, the 489th digit is the very last digit of the number 199. The last digit of 199 is 9. Therefore, the 489th digit is 9.