Printers work by moving from the top left of the paper to the top right, then moving down one line to repeat again. DPI (Dots per Inch) measures how many dots are in each inch of that line, for example 300DPI equates to 300 dots in each inch. Digital displays (monitors, TV's etc.) do not recognise DPI at all and instead display images based on pixel dimensions.
Similar to resolution, higher DPI = more detail. Low DPI is generally used to preserve the amount of ink used and has many applications. For example, a draft copy of an assignment can be printed in low DPI to conserve the ink for the final copy. 72 DPI is classed as low resolution and should not be used for final production though, with 300 DPI+ classed as high resolution and generally speaking should produce good printed results (if the document is already set to the size needed to print).
A higher DPI cannot increase the amount of detail in an image if the original image is low resolution though, so you have to be aware of the resolution of your original image to ensure you are not wasting ink or trying the impossible - finding a small 72DPI image via the internet then increasing the DPI (and/or image dimensions) in Photoshop will only help to reduce the quality of what you originally had.
With this in mind, the simple rule for image manipulation (and creation) is to start big, as it's much easier to reduce a file to work at a smaller size than it is to enlarge one!!
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