Removing scratches from side glass

[EMCD]

I have a few scratches that don't catch my fingernail when I drag past them and one that it looks like some took a diamond ring to. How can I remove the tiny scratches? Any way to remove or minimize the other gouge?

[DoNotChallengeHer]

Toothpaste.

[BS CUDA]

I have a few scratches that don't catch my fingernail when I drag past them and one that it looks like some took a diamond ring to. How can I remove the tiny scratches? Any way to remove or minimize the other gouge?

I was given 4 bars of different colored jeweler's rouge for scratches in my passenger side glass. Someday I will actually give it a go. Here is a link I just looked up that may help.
http://www.howtocleanstuff.net/how-to-remove-scratches-from-glass/