Yes, that's the way Excel treats numbers by default. And that makes sense, generally. After all, most of us prefer to read 2 if they mean 2, not 02 or 002 or 0002.

There are 2 ways around this behavior. And it's up to you to choose one of them:
1. Enter it as a text field by preceding it with a single quote, for example '001
2. Enter it as 1, but give the cell a numeric format with the correct number of digits displayed (include leading zero's). A custom format of 000 will display 1 as 001.