How many copies of the digit 0 are there among the digits of the first 1000 positive integers?

The digit 0 appears 223 times.

There are 9 zeros between 1 and 99 ==9

There are 20 zeros between 100 and 199==20 x 9 ==180

There are 3 zeros in 1000 ==3

Total ==9 + 180 + 3==192 zeros between 1 and 1000 inclusive.