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If I scan in an image at 300ppi and then in photoshop resize the image to 72ppi but want to keep the dimension the the same so say 5cm x 3cm can you do that because I change the ppi to 72 and it says the dimensions in cm is still 5x3 but the image clearly reduces in size?

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The answer to your question depends on whether you are resampling the image or not. In the Image Size dialog, there is an option to switch resampling on or off.

If you don't want to resample the image, then there's no point changing the PPI to 72. Just leave it at 300. If the image is destined for a web page, then web browsers ignore the PPI setting anyway.

If you do change the PPI to 72, but do not resample, then the image dimensions in inches/cm will increase. This is normal. There is no way to make them stay the same if you take this route.

If you resample the image, the amount of pixels will be reduced, and quality and resolution of the image will be reduced, but the dimensions in inches/cm will remain the same. This is normal when resampling.

If you are resampling the image, make sure when you save that you don't overwrite your original image. When you resample, you remove data and pixels, and you can't get them back.

Note: The PPI/DPI influence the output resolution of an image, they are not a measure of the quality of an image. PPI in combination with the image dimensions, controls the size at which the image will be sent to the printer, while DPI is related to the printer output resolution. The PPI or DPI settings are irrelevant for the web. For further reading, there's an old but still relevant article here: The Myth of DPI which discusses what DPI/PPI are, and what they are not.

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