What dpi should I be using for prints?

Question

I usually print photos directly from within Aperture by using the Apple/Kodak 'order prints' system built in to Aperture. However, I have had a few problems with this and decided recently to try using a local vendor instead. I notice the vendor recommends .jpg files with a minimum dpi of 300. When I looked at the export settings in Aperture (under "jpg-original size"), the dpi is set at 72. My questions are:
1) Will changing it to 300 dpi make a big difference?
2) When I've been ordering from Apple/Kodak using Aperture's print service, what settings are being used there? 72, 300 or other?
3) If I give digital files to someone on a CD, should I export at 300 dpi if they intend to make prints? I have, evidently, been exporting at 72 dpi all this time...
I should probably point out that I shoot in RAW, then convert to .jpg when I've done my adjustments and am ready to export to a CD.
Many thanks.

Answer 1

Jamie,
As iDave stated, the DPI number that your picture indicates is not necessarily relevant to your printing process. What is important is how many pixels you have to work with.
That 300 DPI is a somewhat magical number, dealing with physics and human anatomy. At normal reading distance (something like 16 inches?), the average human eye can tell differences if a picture is printed at less than 300 DPI. That is, your eye is can resolve up to 300 DPI at reading distance.
To find the DPI, there is no setting. Take the number of horizontal pixels in your picture (let's say 3000), and divide it by the horizontal size of your photo (Let's say 6 inches if you are printing 4x6). That photo can have 500 DPI, when printed, if the photo printer supports resolutions that high. 500 DPI is greater than 300 DPI, so your eyes will be happy. They will be just as happy as if you had printed with 1800 pixels wide, which is 300 DPI. If you print out a photo that is 1200 pixels wide to a 4x6 print, you will have 200 DPI, and your eye will tell that things aren't really quite crisp.
So, taking the math the other way, if you are printing 4x6 prints, you would want the long dimension to be at least 6x300=1800 pixels. In other words, don't crop a photo to less than 1800 pixels wide and expect it to print sharply. Also, don't use an Aperture export option that reduces the number of pixels ("TIFF - 50% of original size") if your original was less than 3600 pixels wide.
All this math of course has nothing to do with the quality of your original. If your original wasn't in focus, printing it as a 4x6 with 300 DPI will look out of focus. If you threw away a lot of pixels because it's a low quality JPEG, you won't get those pixels back and the photo may look blocky at any size.
This also says nothing about how good your eye really is, too, and how far away you will be when viewing your prints.
Hope this makes sense,
nathan