Question: I have some photos in a standard 2:3 aspect ratio that I want to print and put in a frame. However, all the options for printing as well as the standard frame sizes I found are not *exactly* in a 2:3 ratio, but slightly off. 

For example, here are some standard sizes I found that are suggested by both the photo printing service I use and the frame sizes that are available at some online stores: 

* 9cm x 13cm
* 11cm x 17cm
* 13cm x 18cm

But those aren't actually 2:3 ratios. The exact length for the long side should be `9 x 1.5 = 13,5`, `11 x 1.5 = 16,5` and `13 x 1.5 = 19.5`. So why are the ratios off like that? I first thought it's because of the bleeding or something like that, but that doesn't make sense either since the actual ratio for those formats vary and the cutoff differs between them (as well as between the long and the short edge).

So what's up with those standard sizes? And how will they fit in the frame? I had some pictures printed out at 11x17 cm, I've measured them now and they are actually more like 11.2x17 cm, which is pretty much 2:3 ratio. What's up with that?

For example, for this purpose I would like to get the 13cm frame & print. However, between the mentioned 13x18 format and an actual 2:3 format is some disparity. So what will happen? Will the print service cut the long edge by 1.5 cm? Will the short edge be slightly shorter? Or what?

Answer: 
> 
> So what's up with those standard sizes?
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> 
> 

The dimensions you mention are very close to the B7 (88x125mm), C6 (114x162mm), and B6 (125x176mm) standard sizes, respectively. So I think you're just seeing European standards in action. There's some useful method to their madness -- each size in a given series is [1/2 the size of the next larger size](https://en.wikipedia.org/wiki/Paper_size).

> 
> And how will they fit in the frame?
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> 
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It's a good bet that if Europe has standard sizes for paper, they also have standard-sized frames to fit those paper sizes. You should be able to find frames that fit your prints.

> 
> So what will happen? Will the print service cut the long edge by 1.5 cm?
> 
> 
> 

You'll need to either crop your image to the right aspect ratio, or print the entire thing with white bands on two sides. It's just like printing an image at 5x7in or 8x10in, which people do all the time in the US.
Lots of *stuff* is "not exactly ..." because of historical compromises. Many of these involved adapting something new to something old.