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Proper DPI for different sized images

Obviously if the dots of ink are larger than the pixels, then the printer will be unable to resolve the pixels. But if the dots are smaller, then you'd have to have smaller pixels else they become visible.

A pixel is rendered by multiple dots.
 
The difference in concept between ppi and dpi is relatively new, but it's an important idea to understand. Typically photographers don't need to worry about DPI, the amount of ink dots the printer lays out is more or less constant, and continuous tone printers like dye sub or some wet process printers don't work this way. DPI does become an issue in stochastic offset and lithographic reproduction, but that's more a prepress problem than a photography problem.
 

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