Another way to think about this is this: Would you agree that
1/3 = .33333...? .3333....is the way to write 1/3 using decimals.
If you multiply both sides of the above equation by three you get
1 = .99999...., right?
I think the problem you are having, though, is BELIEVING it
is true, right? I admit, depending on how you look at it, it can seem
false. After all, how can 2 different numbers be equal? The thing is,
these 2 numbers AREN'T different. I think saying 1 = .9999... may
seem contradictory to us because we aren't realizing that .999.... is
a repeating decimal that really does go on forever. Obviously saying
1 = .9 is false, as is saying 1 = .99, 1 = .999, 1 = .9999, etc. But we
aren't dealing with finite decimals here. So, you might think of
.9999.... as another name for 1, just as .333... is another name for 1/3. |