Find & return all non-zero values within a range, on a different sheet

Hi - I have searched and searched for the correct approach to solving my problem and have gotten only close. Any help will be much appreciated.

I need to be able to search a range of cells (one column only), most of which do not have data in them, and have all the non zero values returned on a different worksheet, in a range that's a different size. For example:

Sheet 1 has:

1|
2|
3| .05
4|
5|
6| .02
7|
8|
9|
10| .01

And I need Sheet 2 to show:

1| .05
2| .02
3| .01
4|
5|

For one, the data entered will not always be entered in rows 3, 6 and 10, so it needs to be able to search all the rows. We do however know that there will be no more than 5 data entries (this is the size of the destination range).

Second, the fact that the source range and the destination range are different sizes can't be changed.

Third, Sheet 2 needs to auto-update when a value on Sheet 1 changes. This is why a filter wasn't enough, unless I was just missing something.

If the blank cells are an issue, zeros can be inserted.

Any insight here will be greatly appreciated. I have struggled to find the right formula/function for this and can't find one that meets each of the requirements.

Thank you!

Thank you Andrew for the quick reply. I knew I had left something out - the source and destination ranges don't match - they start in J10 on Sheet 1 and M126 on Sheet 2.

However, if aligning the addresses of the first cell in both ranges is the only way to make it work, I can probably make that happen somehow. I will tinker with it.

Thanks again for your the help!