Wipe Plexiglas with a damp, soft rag. Do not use your hand or a dry rag. Remove the dirt and dust.
Clean Plexiglas with a cleaner designed for Plexiglas. Do not use products with ammonia or any other cleaners designed for real glass. Shake the cleaner well and apply it to a dry, clean cloth. Wipe the Plexiglas clean.
Apply a Plexiglas scratch removing polish to a dry soft rag. There are many Plexiglas polishes on the market. Choose one that is designed for the size and type of scratches on your Plexiglas.
Rub the scratches with the rag as indicated on the label. In general, rub it in a back and forth motion in the opposite direction of the scratches. The rag should always be damp with the scratch removing polish, so replenish as necessary. Keep rubbing until most of the scratches are removed. If the scratches are not buffing out, upgrade to the next level of polish for bigger scratches.
Repeat again with the scratch removing polish, but this time in a circular motion.
Sand Plexiglas to get rid of larger scratches, such those that can be felt with your fingernail. Use a sanding block and a fine grit sandpaper, labeled as 400 grit. Sand over a larger area than the scratch so the Plexiglas is not noticeably thinner.
Switch to a rougher grit, such as 150 grit, if the other one was not working. Next, repeat with a 400 grit, if necessary, and then a 600 grit to smooth the surface.
Wipe the Plexiglas clean with a wet rag and follow up with a buffing wheel, such as one attached to a drill. Use a buffing compound labeled for Plexiglas, gently buffing the surface without pressure.
No