Grrrrrrr you anger me....learn some maths! .9999 recurring IS equal to 1! Hell, I'll even prove it for you if you like -
We all know that 1/3 (a third) can be written decimally as 0.333333 recurring (i.e. the 3s go on forever). It is also obvious that by multiplying a third by three, we get three thirds (3/3) , which is equal to one.
If we look at this same process decimally, take the number 0.33333 recurring and multiply it by 3, and you will see that each 3 in the sequence gets turned into a 9. This gives us .99999 recurring, which, since it is the same as 3/3, is also equal to 1, as explained in the previous paragraph.
The reason for this is that as you add more 9s onto the number 0.9 (after the decimal point), it gets closer and closer to 1. Since there are an infinite number of 9s after the point in 0.99999 recurring, the difference between this number and 1 must be infinitely small, and therefore cannot be any greater than 0.
.999999999~ (recurring) is equal to one because it is .333333~ (1/3) multiplied by 3.
It's equal to one, and the proff is through the way you convert rational repeating numbers to fractions. if you let x = .999999999~ and let 10*x = 9.9999 repeating then 10 x - x = 9x = 9.99999 repeating - .99999 repeating = 9. SO 9x is 9 and x is equal to one. and since we started out wiht x equaling .9999 repeating we know that .9999 repeating = 1.
This could be done with .999999999~ anbd the result would show that .999999999~ = 1
x = .333...
10x = 3.333...
10x = 3.333...
- x = 0.333...
9x = 3
x = 3/9
.333... = x = 1/3
The closest possible number to 1.
Is separated from 1 by the smallest positive number, .00000~1.
Dude, guess what! .999999999~=1!! Isn't that cool!
Dude, go back to middle school please.
1. a repeating number sequence
2. not equal to 1