Why 10/9 = 1.111… ; 9×1.111… = 9.999… ; but 9×10/9 = 10. Why is 10 equal to 9.999…?
In: Mathematics
Numbers are only different from each other, if the distance between them is greater than zero.
What’s the distance between 9.9999 and 10? If you name any nonzero number, the real distance is smaller than that.
If the distance between two numbers is smaller than any number, then you have actually just found two different names for the same number.
Now, how repeating digits work in general, is a little bit more subtle. To understand those properly, you need to approach using the concepts of ‘partial sums’ and ‘limits’. It will help to think a ilttle bit about Zeno’s Paradox (that old story where the runner runs across half the racetrack, then half of the remaining distance, then half of the remaining distance, then half the remaining distance…) Happy to get further into that if you like.
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