Cutting a hole in Plexiglass

Quarter inch would be better for the window aspect. I would scribe the proper diameter hole pattern as Gerald suggests.....then drill a starter hole of about 3/4" with a spade bit out near the perimeter of the circle.

From there I would use a standard hacksaw blade or a Sawzall 'metal blade' with a grip made from friction tape and saw outward to your scribed line and follow it around until cut out.

I would scribe the circle just slightly larger than the pipe needed to get through it.....you can seal around it afterwards with some clear silicone caulk.

Using the type blades I mention and using 1/4" plexi will minimize your troubles. 1/8" plexi can crack and split easily and also 'sag' in the window frame. 

Try and work on top of a blanket or some towels to minimize unsightly scratching.

Thanks Gerald.  Your onto something.  1/8 inch will do if I can't get 1/4 inch done for me for at a reasonable price.  It will just require some time and patience.  I have drilled holes in plexy before so I kind of know what to expect.

Draw a circle the size you need. Then drill tiny holes along that circle. Use a coping saw or RotoZip to remove the center...careful not too much pressure! Sand and file to clean edges.

The other option is to use a hole saw or scribe with a #11 blade the circle using the hole saw bit as a guide until you are all the way through the plexi. Hopefully you are only using 1/8inch plexi.

And lastly, find a piece of metal pipe/duct the same diameter...heat the metal and melt a hole through the plexi by pushing it through. Messy but doable.