Puzzle #2: Odometer

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A car odometer can display any six-digit combination from 000,000 to 999,999, inclusive.  If it runs through its entire range, how many such combinations will have at least one digit 1 in them?

What is the total number of times the digit 1 will be displayed?  (For example, 101,111 contributes five towards the total count of 1's, and the next reading of 101,112 adds four more.)

You are welcome to use whatever method you wish to solve the problem.
Please submit the correct answer by April 1st, 2016.  One $10 gift card will be awarded randomly from those who submitted the correct answer.

Thank you to everyone who submitted an answer (a lot of correct answers were submitted!) but sadly, there can only be one winner.  The winner i
s: Lance Daharsh.