.999~ = 1?

[playa_playa]

Originally Posted by Yoda9864

Well, no it isn't. But enjoy, if you will, a little play on concepts below:

.11111111111 repeating is 1/9 right?
.22222222222 repeating is 2/9 right?
so wouldn't .99999999 repeating be 9/9?

Well, no. Because in math, a number divided by itself will always be 1 (10!/10!=1 in the same way that 10^4/10^4=1). The only trouble is that .111~, for example, will never be expressed in full since its decimal points will be infinite. Therefore, repeating .999~ will never be a precise expression of 1. In other words. at any point you stop adding 9 to the end of the number, that number will deviate from an exact representation of 1. If you are being anal, 9x.99999999~ does not exactly equal 9, no matter how you slice it. It'll just be 8.99999~. It's just that as the numerator approaches the denomenator in value, the absolute value of the fraction itself will infinitely approach 1 - in this case, .999999~.

But this is all just a mathematical triviality, don't you guys think.