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The numbers 10, 20, ..., 1000 end with a 0. There are 100 of these numbers.
The numbers 100, 101, ..., 109, 200, ..., 209, 300, ..., 309, ..., 908, 909, 1000 contain a 0 in their tens column. There are \(10\times9+1=91\) of these numbers.
The number 1000 has a 0 in its hundreds column.
In total, there are 100+91+1=192 zeros.