Zeroes

I've never hated someone as I hate you and your exercises. No that way, but... Damm, I almost wrong this one. I wouldn't forgive me.

This is my solution, I hope my English is understandable:

Separate the big number in three parts: Unit, Ten, Hundred.

Unit: every $10$ numbers, we have $1$ 'zero'. So $1000$ numbers, we have $100$ 'zeros'.

Ten: every $100$ numbers, we have $10$ 'zeros'. Since we start to count it from $100$ to $1000$ , from $10$ to $999$ we have $90$ 'zeros', when $1000$ we have $91$ 'zeros'

Hundred: only one zero.

Sum the results : $100+91+1 = 192$