Boe, you are saying the opposite...
PPI is pixels per inch. This is what most people really mean when they say DPI.
A digital image normally only have pixels. It does not "have" a DPI or PPI. It might have a DPI number inside, but that number is nearly useless.
(Note: I just read the JPEG is the only image format containing a field for DPI!)
If you have an image that is 2000x2000 pixels and print it at a size of 2x2 inches you print it at 1000 PPI. If you print the very same image at a size of 5x5 pixels you print it at 400 PPI. The DPI value inside the image might still just say 72 DPI.
Now, when printing a pixel the printer needs to be able to give the pixel a certain color. However the printer only contains a finite number of inks, each with it's own color. To be able to give the pixel the desired color the printer must print one pixel using several dots. This becomes the DPI value.
For example a 1200 DPI inkjet printer will usually only be able to print 300 PPI, while using 4x4 ink dots for each pixel.
Look at the illustration on this page.
http://mydigitalcamera.us/ppi-vs-dpi-resolution-what%E2%80%99s-the-diff/This means it is virtually impossible to print a 300 PPI image with less then 300 DPI (some types of printer can print a pixel using just one dot where they mix different amounts of the inks).
Found another page with some better illustrations and more info
http://99designs.com/designer-blog/2013/02/26/ppi-vs-dpi-whats-the-difference/