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

The correct option is 9.

To find the 489th digit in the concatenated sequence of natural numbers 123456789101112..., we can break down the counting process by grouping numbers according to their number of digits.

Step 1: Count digits from 1-digit numbers
The single-digit numbers are 1 through 9.
Total 1-digit numbers = 9

$\text{Digits from 1-digit numbers}=9\times 1=9$

Step 2: Count digits from 2-digit numbers
The two-digit numbers range from 10 to 99.
Total 2-digit numbers = $99-10+1=90$

$\text{Digits from 2-digit numbers}=90\times 2=180$

The cumulative number of digits written up to 99 is:

$9+180=189\text{ digits}$

Step 3: Calculate the remaining digits needed
We need to reach the 489th digit. Subtracting the 189 digits used by 1-digit and 2-digit numbers gives:

$489-189=300\text{ digits}$

These 300 digits will come entirely from 3-digit numbers starting from 100.

Step 4: Identify the exact number and digit position
Since each 3-digit number contributes 3 digits, we divide the remaining count by 3:

$300÷3=100\text{ with a remainder of }0$

This means the 489th digit is the very last digit of the 100th 3-digit number.
The 100th 3-digit number is:

$99+100=199$

The digits of 199 are 1, 9, and 9. Since the remainder is 0, we select the 3rd (final) digit of 199, which is 9.