Photo size corresponding to the mentioned sizes are:
3R = 3.5" x 5" (1,050 pixel x 1,500pixel)
4R = 4" x 6" (1,200 pixel x 1,800 pixel)
5R = 5" x 7" (1,500 pixel x 2,100 pixel)
6R = 6" x 8" (1,800 pixel x 2,400 pixel)
8R = 8" x 10" (2,400 pixel x 3,000 pixel)
S8R = 8" x 12" (2,400 pixel x 3,600 pixel)
10R = 10" x 12" (3,000 pixel x 3,600 pixel)
S10R = 10" x 15" (3,000 pixel x 4,500 pixel)
It is not related to the magnification (or zoom) percentage in Photoshop.
We only have so many pixels in our digital camera file or scan. The larger we print an image, the further we have to spread out these pixels. It’s like having a room to paint and trying to use a pint of paint when a gallon would be better. We may be able to get some color on the wall from the pint-size can, but it will be a thin coat, and probably won’t look very good. Instead, if we choose the gallon size, we can get good coverage and the color will look thick and strong.
That’s the question the photographer really wanted to know: How far can I spread the pixels out, and still make a good looking print?
There is no simple answer to this question because it depends on what device you are printing on, the subject matter, and what you think is acceptable quality. However, there are some benchmarks that will help you recognize when you'll be degrading the quality of the image. Let’s look at the benchmarks for two common printers:
Chromira and LightJet printers:
These printers make excellent quality prints from 200 dpi files. Even though their native resolution is 300 dpi, through sophisticated built-in interpolation and the use of photo paper, 200 dpi is more-than-enough to make prints 16x20 and larger. Whenever you drop below 200 dpi, you will start to see a degredation in quality. How much depends on the subject matter and the size you are printing.
I recently made some 24x32 prints from the Canon 1Ds MK II 16-megapixel camera, and the original 1Ds 11-megapixel camera. The prints were made at 128 dpi and 105 dpi, respectively, and they looked very good. When compared to prints from film, there was a noticable loss of resolution, yet they still held up surprisingly well. This means prints made at 100 dpi can still look good--but the quality isn’t the same as printing from 200 dpi files. When making prints at less than 200dpi, you'll need to test the different resolutions yourself to see what meets your expectations.
Epson 9600 printers:
My experience is that any time you give the Epson 9600 less than 360 dpi, you will see noticeable jaggies in the image. This is particularly evident in text. 360 dpi is a serious amount of resolution. Fortunately, there is a trick to help us use smaller-resolution files.
My testing shows that if you have a file smaller than 360 dpi, you can make a better print by interpolating the file up to 360 dpi using Photoshop. So, let's say you have a 240 dpi file. If you printed it as-is, you would see some jaggies in the print. But if you take that same file and use Photoshop to size it up to 360 dpi, it will not have jaggies, and the print will look sharper than the original 240 dpi file.
Using this trick, I have found that all I need for the Epson 9600 is a 240-dpi file. Having more resolution doesn’t increase quality, but if you use less than 240 dpi, you will start see a decrease in quality. For critical applications, you'll need to test the resolutions yourself to see how it meets your expectations.
Is that your final answer?
Now that we have all of this knowledge, let’s ask the question again: How far can I spread the pixels out, and still make a good looking print?
A 3008 by 2000 pixel file will create prints in the following sizes:
My experience is that most photographers who haven’t used medium format film or larger would find the 20" by 30" acceptable. For photographers who have used medium format, anything larger than 10" by 15" will begin to fall short of your expectations.
If you need more of an answer than what I've spelled out here, your best option is to make test prints of your files, using different resolutions. Use our print lab to test your prepared files on both the Chromira and the Epson 9600. Seeing your own images printed at different resolutions is the best way to answer your resolution questions for good.