SOLUTION: Dr. Math was numbering the pages of her scrapbook with consecutive positive integers, 1,2,3,..., in decimal notation. When she wrote a page number with three digits, shed wrote the

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Question 380080: Dr. Math was numbering the pages of her scrapbook with consecutive positive integers, 1,2,3,..., in decimal notation. When she wrote a page number with three digits, shed wrote the hundreds digit first,then the tens digit, and finally the units. She was interrupted after writing the 1832nd digit. When Dr. Math continues, what digit should she write next ?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Note that there are 9 one-digit numbers, 90 two-digit numbers, 900 three-digit numbers, etc. in base 10.
The first 9 digits are used to number 1-9. Then, 180 digits are used to number pages 10-99. This is 189 digits total, leaving 1,643 digits left. 1,643/3 = 547 R2, so 547 three-digit numbers will be completed, then two more before Dr. Math is interrupted.
The 547th three-digit number is 646 (note that the set is inclusive), so she will write 646, 64_ so the next digit is 7.