1002
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Provided that the first digit cannot be 0, 1000 is the smallest number with four digits. Otherwise there are smaller numbers with 0 to thousandth digit such as 0100, 0050. The smallest integer in such instance is 0000.
That would be the same as the smallest four-digit even number: 1,000, which also happens to be the smallest four-digit whole number.
If you allow non integers, then your smallest four-digit number would be .0001. If you only allow integers, then your smallest four-digit number would be 1000. Your largest four-digit number would be 9999.
The smallest four digit number is 1000. It is even so 1001 is the smallest four digit number that is odd.
The smallest four-digit number not using zero is 1000. In a four-digit number, the first digit cannot be zero, so the smallest possible value for the first digit is 1. The remaining three digits can be any number from 0-9, so the smallest possible four-digit number is 1000.