I am a bit confused about this. For instance, the word for “king” would be written as おう in kana, but the word for “ten days” would be とおか, right? What am I missing here? Is there a rule that I don’t know about?
It is mostly a historical thing. I haven’t really found a rule about it. Just memorize it.
In case of とおか、I think it is derived from とお(十) ten things.
There is also 通 which has the same kun’yomi.
That is all the ones I know from memory. Most of the times that long ō is written as おう、よう、とう、こう and so on.
The rule is “words that were once written as ～おほ or ～おを are now written as ～おお, while ～おふ became ～おう”. But yeah, unless you’ve got a master’s degree in Japanese etymology, “just remember them as you encounter them” is the better method.
Like @Saida said, it’s ～おう more often than not.
I think I’ve mostly seen おお when part of a kun’yomi reading like 氷(こおり) and おう when on’yomi like 人工(じんこう).
Just knowing that there is a solid etymological reason for the difference will help me sleep tonight. Thanks.
I can venture to guess that at least one of the dialects will pronounce the two slightly differently, perhaps?