I have to make a rant about this. It's a plauge.
You send someone a rasterized image (an image made up of pixels, not paths). They come back and you and say "It needs to be 300 dpi." And that's all they give you. If that's the case you need to send them here.
A pixel is like a dot. 1 pixel = 1 color. Millions of pixels make up a giant mosaic that makes a picture. That's a rasterized file a giant moasic. Paths scale so you don't need to worry about those.
Anyways all they tell you is "It needs to be 300 dpi." Well unitl you tell me the end print size or display resolution of the device. How do I know it's not 300 dpi. DPI is a print term, Dot Per Inch. How many color dots is the printer going to make in every inch of surface.
A device such as a tablet or computer monitor has PPI, Pixels Per Inch. How many color cells can it fit in one inch of the display device.
To get to the point if it's a 2500 pixel wide image. It will print up to 300 dpi at (2500 / 300) = 8.33 inches wide. So printers if you know it needs 3 inches wide when it prints say "Hey can you send it at least 1500 pixels wide. Most of all if it's not getting off a screen and actually being printed. STOP USING DPI. You're not using DPI. If you're aiming at using the graphic for a particular device you should be using PPI and you already know how many exact pixels it should be.
If you're not talking to the person printing it stop using DPI. Please.
Ok I think I'm done.