While observing the typical number representation theory I came up with this weird observation. While we represent the higher order of exponents towards the right side of the number line representing numbers we follow opposite, i.e., higher order exponents are written towards the left side, i.e., we flow from left to right. Why is this? Is there a scientific explanation? e.g., You know $123$ is $3(10^0) + 2(10^1) + 1(10^2)$. In number line $10^2$ is right to $10^1$ and $10^1 $ right to $10^0.$ So if we follow number line the representation could be $321$ to represent $123$, but we do represent in the opposite way. Why is this?
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Welcome to MSE! It would be easier to read your question if you used Mathjax – J. W. Tanner Jan 28 '19 at 13:53
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Yes, I'm trying to learn the tools and methods to post more efficiently in this forum. However, this question was bugging my head for the past day. So I was in a hurry. Thanks anyway. – user3345621 Jan 28 '19 at 14:37
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Interesting question. I don't think the answer is, "because in English we write from left to right", because our value of 123 could be written as 321, and this 321 could be considered "left-to-right" if we defined 321 as 3*10^0 + 2*10^1 + 1*10^2.
Another example could be the number 14.67 = 0.07 + 0.6 + 4 + 10. But there's nothing saying we couldn't instead define from the outset 76.41 = 0.07 + 0.6 + 4 + 10.
I think the answer to this question is: it's arbitrary how we define how numbers are written, and your way would technically work just as well as the common way. However, people have stuck with what was first done (if it ain't broke, don't fix it) and it's easier if everyone sticks to the same convention, even if your way is equally valid.
Furthermore, if people commonly used both ways then for example, I could see how kids might get confused or even give up learning long division the two ways, which would be counter-productive.
Adam Rubinson
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