Should it not be い かい as I thought the counter for floors was -kai ?
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It should be いちかい, not い かい if you thought the counter for floors was -かい. – Rathony Oct 26 '16 at 13:04
Because of 促音便, the pronunciations of いち, ろく, はち, じゅう, ひゃく change to いっ, ろっ, はっ, じゅっ/じっ, ひゃっ when followed by some counters, like this:
いち + かい → いっかい (1回/1階)
ろく + かい → ろっかい
はち + かい → はっかい
じゅう + かい → じゅっかい
ひゃく + かい → ひゃっかいいち + こ → いっこ (1個)
ろく + ひき → ろっぴき (6匹)
はち + ほん → はっぽん (8本)
じゅう + ふん → じゅっぷん/じっぷん (10分)
いち + てん → いってん (1点) -- but 6点, 100点 are ろくてん, ひゃくてん
はち + さい → はっさい (8歳) -- but 6歳, 100歳 are ろくさい, ひゃくさい
etc...
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1This sound change occurs when the counter word starts with か行(k), は行(h), and for 1, 8, 10 with さ行(s), た行(t)... I think. – Chocolate♦ Oct 26 '16 at 13:41
It is a phonetic transformation similar in English to "aren't".
Instead of saying "are not", you can say "aren't".
Instead of saying "いちかい", you say "いっかい".
The difference is that in Japanese the pronunciation is not optional. You have to say いっかい. It is wrong to say いちかい.
Most of these words are listed in dictionaries and in good grammar books.