If you write the numbers 1, 2, 3, ..., 10, 11, 12, ..., 99, 100, ..., what is the 1000th digit you write?
+310 Let's use casework.
From 1-9 there are 9x1= 9 digits
From 10-99 there are 90x2= 180 digits
So far we have 180+9=189 digits. Now we have to start breaking it down into smaller cases.
From 100-299 there are 200x3=600 digits
This is not enough. We need 1000-(600+189)=211 more digits
Since we are in the 3 digit number region, lets divide 211 by 3. This equals 70 with a remainder of 1. We add 70 to 299 to find the last number.
So that means from 1-369, there are 999 digits. The next digit, the 1000th digit, is 3.
