Yes. It’s most natural to break out んです as a response or explanation. It helps to look at what’s happening grammatically here.
んです is really just a contraction of のです, the same ending の that you might know as a nominalizer. Ex. 泳ぐのが好きです. (“I like swimming.” Lit. “Swimming is liked (by me).”
泳ぐ (swim) —> 泳ぐの (swimming)
So when you say something like 十円足りないんです, it’s the same as 十円足りないのです (though that’s awkward and unnatural). Or, to translate it to reflect the grammar/nominalization:
“It’s that I’m 10 yen short.”
(With 足りないの actually being a noun phrase: “being insufficient” or “(the fact) that it’s insufficient.”)
This is also why the phrase takes on です instead of ending with the verb. The last part of the sentence is a noun, so you need だ or です.
If you think about it along the lines of, “It’s that I’m ten yen short,” it becomes more clear why it’s more natural as an explanation or response than a stand-alone statement.
(Note that the phrase is also more natural in Japanese than “It’s that I’m ten yen short” is in English, so this is really just to illustrate the nuts and bolts of the grammar/logic, rather than the feeling. Unfortunately the languages rarely line up in terms of grammatical logic and natural use, which is why I think it’s helpful to have both the practical equivalent in English and the transliteration sometimes. One to help you remember when to use the phrase, the other to help you understand why it is the way it is.)
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