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I have scanned a document into a PDF at 300dpi. The document file is larger than I would like. Is there a simple way to down-sample the document so that it has a lower resolution? Or do I just need to re-scan the original document?

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You can use ImageMagick's scale or resize operators.

ImageMagick® is a software suite to create, edit, compose, or convert bitmap images. It can read and write images in a variety of formats (over 100) including DPX, EXR, GIF, JPEG, JPEG-2000, PDF, PhotoCD, PNG, Postscript, SVG, and TIFF.

For example, from a terminal:

convert input.pdf  -resize 50% output.pdf

or

convert input.pdf -scale 50% output.pdf
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Apple's Preview comes with a feature allowing you to save a file with a reduced file size.

Open your file in Preview, and click File>Save As.

Scroll down to the bottom where you will see a "Quartz Filter" drop-down menu and choose "Reduce File Size".

If you want to retain a copy of your original but larger file size, rename this file and click save. Otherwise you will overwrite the larger file when you click save.

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    I have very bad experiences with this tool. There is little control for the user as to how much the resolution is lowered. In most cases, the text pdfs that I use are unreadable when applying this filter.
    – gentmatt
    Apr 26 '12 at 18:51
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    If you aren't afraid of some harmless XML editing, you can create custom quality size reduction filters for Preview. macworld.com/article/1168311/software/… explains how.
    – hendrik
    Feb 9 '17 at 9:48

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