What does “a million” mean?
The obvious answer is that it’s “1,ooo,ooo”, however that quantity is expressed in your language of choice.
To many language learners, the answer to a question like “what does this word mean?” can only ever be a word in their first language. In Japanese English education, the “meaning” of a word is synonymous with its translation. The only correct answer in this view is 百万 hyakuman or “100,0000”. I mean to point out here that this is only one aspect of that word, or any word, and in many cases more salient characteristics of a word are its role in discourse (playful exaggeration) and just how easy it is to say. Learning to speak a language the way native speakers do entails prioritizing these characteristics in somewhat the same way they do, and not fixating on an atomistic view of words in which their only definitions are precise and mathematical and shorn of the vagaries of context and collocation.
Did you notice the odd comma placement in that number in the last paragraph? That comma is where it is for good reason. Big numbers in Japanese (presumably also in Chinese) are grouped together in units of 4 digits. You have to get to 1,0000 (one man) before you start reusing old denominations to add more zeroes a la “ten thousand” or “one hundred million”. Hyakuman means one hundred man, which is 100 of 1,0000, or 100,0000. You have to get to 100 million before you get to another number that can be referred to with a single word in Japanese – oku, or 1,0000,0000. (The next denomination happens to coincide with the English trillion, 1,000,000,000,000, or 4 groups of 3 0s; as 兆 chou, 3 groups of 4 0s, or 1,0000,0000,0000. You usually only see this one on the news in reference to public debt.)
If that’s rather confusing, consider then that preschoolers in the US routinely use the word “million”, whereas preschoolers in Japan do not as frequently say hyakuman. If the words are synonymous, and the underlying concept is any both cases difficult for preschoolers or anyone else to grasp, what accounts for this?
Well, first “million” is a difficult concept in only one sense but in any case a fun word to articulate. Taken not as an expression of formal mathematics but as an analog expression of intensity, it expresses the idea of “a really big amount” without forcing either the speaker or listener to do any computation. It also starts with a phonologically easy bilabial stop. Ditto for “billion”, and in my view that’s why preschoolers use those two words more or less interchangeably. Hyakuman is only the same in the formal mathematical sense – it doesn’t have the simplicity of a single morphological unit like million and therefore most likely takes a bit more mental work to understand, nor is it as phonologically simple, even by the standards of normally multisyllabic Japanese words.
In the corpus treated by the Japanese concordancer Shonagon, 億 oku appears 20972 times and 百万 hyakuman 4611 (万 man by itself 70173 times, 兆 cho 6190 times). These results square with the commonsense view articulated above, that factors other than mathematical simplicity dictate the use of these terms. One can imagine that if computers spoke to each other in a more human sense, they might prefer #AAAAAA to #0F4240 as an expression meaning “a huge amount of”. The second of those equates to 1000000 in decimal, by the way.
So if translation is the art of taking words from one language and reproducing the idea represented by those words in another, hyakuman cannot be a good translation of million unless we are talking about math or economics. In most senses of translation that are important to us humans, million can’t even be said to be a perfect translation of 1,000,000.