This is a discussion of the vagaries of floating point math, on a forum for programmers. I would expect that most folks learned something about how to carry out decimal long division in ~3th–6th grade sometime.
If we can’t assume any kind of common base-line level of background experience but need to re-hash all of school mathematics in every conversation, then it’s hard to have a technical discussion.
There’s absolutely nothing wrong with not having an understanding of this point, or forgetting grade school arithmetic, and I’m not trying to be condescending, but it seems weird for the top-level poster to call out the the article’s language. The idea that some fractions don’t have a terminating decimal expansion is “pretty simple” in the context of any reasonable standard for discussion among programmers.
Here’s the language from the article. Is it really that confusing?
> When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals.
If the top-level poster was confused and wanted help, he/she could have said something like “Can someone explain this point to me? I don’t understand what it means for 1/7 to be a ‘repeating decimal’, or what a ‘prime factor of the base’ means.”
>If we can’t assume any kind of common base-line level of background experience but need to re-hash all of school mathematics in every conversation, then it’s hard to have a technical discussion.
We can have any kind of discussion we want, but whatever the participant's level of understanding, talking down to them is unacceptable. You don't need to dumb things down here, but when someone doesn't understand what you meant, you can ignore it or help out, just don't be condescending.
If we can’t assume any kind of common base-line level of background experience but need to re-hash all of school mathematics in every conversation, then it’s hard to have a technical discussion.
There’s absolutely nothing wrong with not having an understanding of this point, or forgetting grade school arithmetic, and I’m not trying to be condescending, but it seems weird for the top-level poster to call out the the article’s language. The idea that some fractions don’t have a terminating decimal expansion is “pretty simple” in the context of any reasonable standard for discussion among programmers.
Here’s the language from the article. Is it really that confusing?
> When you have a base 10 system (like ours), it can only express fractions that use a prime factor of the base. The prime factors of 10 are 2 and 5. So 1/2, 1/4, 1/5, 1/8, and 1/10 can all be expressed cleanly because the denominators all use prime factors of 10. In contrast, 1/3, 1/6, and 1/7 are all repeating decimals because their denominators use a prime factor of 3 or 7. In binary (or base 2), the only prime factor is 2. So you can only express fractions cleanly which only contain 2 as a prime factor. In binary, 1/2, 1/4, 1/8 would all be expressed cleanly as decimals. While, 1/5 or 1/10 would be repeating decimals.
If the top-level poster was confused and wanted help, he/she could have said something like “Can someone explain this point to me? I don’t understand what it means for 1/7 to be a ‘repeating decimal’, or what a ‘prime factor of the base’ means.”