I work at 300-400 dpi, and I work MUCH larger than 940px wide. Grassblades currently uses a 3307x4677 canvas size, and then I scale it down for posting. That means I can work with a great amount of detail, while all the tiny mistakes I make get hidden when I scale stuff down.
I've always worked in bigger sizes than I post - it's in case I ever want to print it. If I work in smaller sizes, they might look grainy and terrible if printed. Larger sizes means I avoid that. The rule of thumb for print is to ALWAYS work in a bigger size than you intend to print. Also, 300 dpi is the accepted standard for print, AFAIK - while 72 dpi will do for web-publishing.