No.
1000 has 4 digits and is the smallest 4-digit number.
The smallest 3-digit number is 100.
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The smallest four digit whole number is 1000.
4500
Smallest when rounded: 4500 Smallest when rounded down: 5001
1000
This depends on what you mean by smallest. The smallest four-digit whole number is 1,000; the smallest four-digit real number is .0001 (1/10,000); the smallest four-digit integer is -9,999.