I'd say it's strictly a conversational ploy to stress that you're too lazy to specify exactly what restaurant you're talking about, but you hope the people you're addressing will know which one you mean.

  - A.

Restaurant A.  Restaurant B.

Here: This restaurant.  There: That restaurant.

Here:  This restaurant.  There: The other restaurant. 

_______

10.  Half of 10 = 5.

20.  Half of 20 = 10.

50.  Half of 50 = 25.

______

--  How would you rate Restaurant B on a scale of 1 to 10? 

--  I think I would rate it 10!!!  It's very, very good.

--  How would you rate Restaurant A on a scale of 1 to 10?

-- I think I would rate it 4.  It's not very good.

-- Hmmm.  Half of 10 is 5.  You have rated Restaurant A less than 5.  You rated Restaurant A as 4. That's less than half of your rating for that other restaurant -- Restaurant B. 

-- Yes. Restaurant A was not half as good as that other restaurant.  It was less than half as good as Restaurant B.

______

CJ 

Thank you Avangi very much,I understand the phrase "not half as" now , but I am still confused about why THAT can be used before OTHER . It's sounds strange to me . I 've ever heard "The other restaurant ..." I 've never heard "that other restaurant " .

By the way , please check that my sentences below are correct:

a/Imitation goods are about eighth-tenths of the quality of our authentic goods.

b/This restaurant is good as well , but it is only about seven-tenths of the restaurant I went to yesterday.  

Best wishes

"That other" is a common form of words; there's nothing strange about it. Generally speaking, and in my opinion:

"The other" is more likely to be used when there are only two possibilities in the frame, and the context has eliminated one. "The other" is then the other one.

"That other" is more likely to be used when there are many possibilities. Context has eliminated one or more of these. "That other" then refers to an unspecified one of the remaining possibilities. The reason it's unspecified could be because it's clear from the context what's being referred to, or because the speaker doesn't know how to identify it (e.g. he's forgotten what it's called), or doesn't want to identify it.

I stress "more likely", as these are just general tendencies, not hard-and-fast rules. There are almost certainly other usage patterns and subtleties that I can't bring to mind offhand.