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Let's do this number by number...

 

There are 10 1's in the ones digits... 01, 11... 91

There are 10 1's in the tens digits. Thus we have 20 for 1's.

 

There are similarly 20 for 2, 20 for 3...

 

Thus we have 20(1+2+3+4+5+6+7+8+9) = 20*45 = 900

 

I believe that is the answer.