I’m not sure what you’re getting at here. I think most (Like here, for instance) would say that recurring and repeating are the same thing. To you, it seems that “repeating” means that the repeating portion starts immediately after the decimal point. Is that correct?
If you just multiply that number by a power of ten, then the repeating part will be moved up to the decimal point. All that means is that the number n must have some factors of 2 and/or 5–which is sorta fundamental, I guess.
Recurring means that some portion of the decimal repeats endlessly. Repeating means that the whole of the decimal repeats endlessly. If your rule is true, then there is no logical way that you can determine what you have to multiply the result by in order to get to the repeating part. To get 1/12 to work according to your rule, you must multiply by 100. Another example is 1/24 = 0.416666*. You have to multiply this by 100 to get your rule to work, but for 1/36 you’re back to multiplying by 100.
sorry for the typo above. should read
Another example is 1/24 = 0.o416666*. You have to multiply this by 1000 to get your rule to work,
What rule? I was just trying to see what you meant by recurring and repeating. I still don’t see any difference between what I said and what you give there.
If I’m following what you are doing in those examples, it’s pretty simple: take the highest power of two or five in n, and multiply by the nth power of 10.
I keep forgetting: Is 2 a prime number? If so, that would blow rampisad’s theory.
Actually, I wasn’t going to post at all, but I noticed that the thread about the number 5 had 23 responses. This must be significant…