Define projection not working

[AngélicaObregónOchoa]

I was using ArcMap 10.5 in the desktop version and started having issues with the projections of my shapefile layers. When defining the projections, they didn’t match spatially. Upon checking the properties table of each layer, I noticed an inconsistency in the extent information. Although the geographic coordinate system and projection information were the same, the extent values had a different number of characters. One layer has two to three digits in the integer part, while another layer has up to eight digits in the integer part. How can I fix this?

The solutions I’ve tried that didn’t solve the problem are:

1. I created a new coordinate system to adjust the false north, east, and west, but it didn’t work.
2. I updated and switched to ArcMap 10.8, but the issue persists.
3. I reprojected the layers in R, but the issue still remains.

Please help me.

[VinceAngelo]

It's usually the case that you should not ever need to Define a projection. The only case where this is appropriate is when:

1. The existing coordinate system is wrong, and
2. You know what the correct coordinate system is.

It's not clear from your attachments (which really ought to be embedded inline) which datasets are which. It does look like two of them may be in geographic (angular) units (the extents look like degrees).

Altering the false origins is useless in this context.

You need to identify which sources were corrupt before you got them, and which ones you corrupted with an ill-advised Define Projection. Once you've got that straight, you need to Project the sources to the desired coordinate reference, not clobber the existing correct metadata.

- V