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You need to think of your monitor and printer as two separate pieces of hardware. What you see on the screen is hardly ever what you get in terms of color accuracy and print quality. You get the colors to match as close as possible by calibrating your monitor to your printer.

300dpi is typically the limit the human eye can see at a couple feet, which is why it is often used as a baseline for print quality.

Overall it depends on the quality of your monitor as well as the quality of your printer. I would recommend printing test strips to see what the result will look like without committing to a full print.

R