Valerii Kryvchyk

I mean yes, It is true that you can't put another non-recurring number after the recurring one but in this case, I use it as an infinitestimal to show that there is still a remainder from the answer but that there is atom-size number that still exists but is not shown as 0 as 0 is nothing. My point is that there is still a remainder from 10/3 but it is so tiny we cant write it out fully but it still exists.

Honestly, I think it doesn't as it is rounding of an infinite amount of 9s into a closest number. Like if we had 3.333 + 3.333 + 3.333 we would have a 9.999 or if we take to 7 significant figures it would be 3.333333+3.333333+3.333333 and it would be 9.999999. This just shows that you can put as many numbers as you want and add them up so in fact it would equal to 9.999999... as 3 + 3 + 3 is 9 and the same thing will continue to infinity. I kind of understand what do you mean but in fact, my expression with 𝜐 would just be perfect without any rounding. But i understand what do you mean and I just think more about the perfect expression. If you have any questions please reply. Thanks!

Hello everyone, For several days I have been thinking about the fractions like 10/3 and 100/16. Calculations show that when you do these problems, usually you would think about the recurring numbers at the end. However if we do the reverse action, the answer won't really equal to the first number we took the result times from the Second number. This is due to remain from the recurring numbers being taken away from the first number. Let's take for example this problem: 10 / 3 (to 1 significant figure) From this question we see that this is going to be a recurring number as any number that isn't a multiple of 3 - will definitely have recurring end. However this problem says to solve to 1 significant figure. So literally the answer will be 3. However, where does the remaining 1 go? It is likely that this question either has no proper answer or has a remainder hidden from answer like 3 and 1 remaining. or we will just have 3 as a proper answer like a calculator would answer this question. The real answer to the problem from these two would be the first one, with 1 remaining. However, it is too tiring to write 1 remaining and if a calculator would be asked that question; he would never answer with such a long answer. So there must be a simple and understandable answer. Let's have another problem: 10 / 3 (to 3 significant figures) From this question we could get the answer of 3.33. This would be quite correct and it would be both useful in calculators and in writing out. But nobody said that this question can't have a long answer like and 0.01 remaining. This answer would be less popular in use but would also be correct. And it would be the only correct answer as the first one doesn't show the remainder. Anyways, we still have to find the simple way to correctly and simply express the remain. Actually, you can put as many significant figures as you want to make yourself happy. However, if you express your answer the short way, you would get an incorrect result when checking the answer. You can still put as many significant figures you like but when using the short way - You would get an incorrect outcome. Here is the reason: 10 / 3 (to 7 significant figures) My answer is expressed in short way as 3.333333 Let's check if we got this right: 3.333333*3=9.999999 Wow! Our outcome is not equal to our first number. But why? Because our answer was expressed incorrectly! Now let's correct our question and do it the long way: 10 / 3 (to 7 significant figures) My answer is now corrected and expressed in a long way as 3.333333 and 0.000001 remaining. Let's check if we got it right this time or not: 3.333333*3+0.000001=10 This is a correct answer! But as we can see it, the numbers are way too long and we have to express it somehow shortly. Here is why we have recurring symbols: 3.(3 recurring) * 3 = 9.(9 recurring) 9.(9 recurring) is not equal to 10 10 - 9.(9 recurring) = 0.(0 recurring)1 So at some point at this type of problems we always going to have the rest and the rest is expressed much better over here. But I have made a better and maybe the best way to express the rest in the problem. I introduce you to 𝜐! 𝜐 is a new simple way to express the rest bit of an improper fraction! From now on, you can express the improper fraction result with Greek letter upsilon = 𝜐. Now, the answer may look something like this: 10 / 3 (to 3 significant figures): 10 / 3 = 3.3 + 𝜐 Now check if it correct: 3 * 3.3 + 𝜐 = 10 So actually, this symbol works as it should! Now, let's try another fraction: 100 / 16 (to 1 significant figure) 100 / 16 = 6 and 4 remaining 4 remaining = 4𝜐 100 / 16 (to 3 significant figures) 100 / 16 = 6.66 + 4𝜐 Now, we can see that 4 remaining is equal to 4𝜐 just like x + x + x + x = 4x. Also this theory can be used on a circle diagram where if we divide it by 3 it will have 2 equal side and 1 tiny bit bigger side. To express the circle remain: 100 / 3 = 33.(3 recurring) + 33.(3 recurring) + [33.(3 recurring) + 𝜐] I believe that introducing and using upsilon (𝜐) in maths will help understanding the fractions and converting into decimals. Providing a fresh and simpler perspective into the related topic. If you have any questions on my thought I am free to discuss the benefits or problems of upsilon. Feel free to Ask me anything about 𝜐! Kind Regards, Valerii Kryvchyk.