It doesn't matter, whenever you multiply something by 10, you essentially move the decimal point forward one, therefore having, in simple terms, one less number on the right and one more number on the left.
You can't just bring extra decimal places out of nowhere.
x = 0.999
10x = 9.99 (Type in 0.999 x 10 into your calculator in case you're confused.)
10x - x = 9.99 - 0.999
9x = 8.991
x = 0.999
Same logic with four or more decimal places
x = 0.9999
10x = 9.999
10x - x = 9.999 - 0.9999
9x = 8.9991
x = 0.9999
This is the logic behind this situation.
X = 0.9999...
10X = 9.999...
10X - X equates to 9.999... - 0.999...
Since we're working with subtraction, we must make sure we align the decimal points.
Ergo:
9.999...
-0.999...
________
9.000...
We've essentially removed the repeating decimal to get nine.
Now back to the algebraic expression 10X - X.
We've already deduced that this equals 9.
This expression simplifies down to 9X (10 plus negative one is nine.)
So one would assume that 9X = 10X - X which, as we saw, was equal to 9.
Following this, we have the expression 9X = 9.
Standard algebra tells us to isolate the variable X.
We do this by dividing both sides by 9, giving 9X/9 = 9/9
This simplifies to X = 1.
Now for the explanation at the heart of this seemingly confusing problem. The error lies in the fact that the decimal repeats indefinitely. The reciprocal of X is a 1 followed by an infinitely small decimal point. The fact is that simple algebra cannot handle this equation. This falls under the field of calculus.
That's actually not true. Mathematically, 0.9 (recurring) is equal to 1. Before you get angry and start thumbing me down because that doesn't make sense to you go and look it up somewhere reputable. It's always bugged me, but it's true.
Actually, wiki is quite the reliable source as far as maths and physics go. Some top authors even put the links to wikipedia in their books for referance.
dude im 19 and in college sry if im not the biggest math buff on the planet and didnt equate the two, but i did find something in polymathematics and it explained it so now i know. i guess you do learn something new everyday. but from my past learning no teacher has ever told me or a class at large that 1=.9 recuring. watch my multivariable calc teacher tells the class this in the first lesson.
******* peons thinking they can troll. Now me, I stay clear of maths. Far too easy to prove me wrong. Trolling with bio is funny as **** though cause evolution has been trolling us for eons
I once was complaining about movie theaters on FB, and at the end I said eh, just some white people problem ranting. got a comment from a girl calling me a racist biggot, etc.