1 = 0.999? How can you prove that 1 = 0.999999999999999999....?
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briefcaseTeacher (K-12)
calendarEducator since 2011
write3,179 answers
starTop subjects are Math, Science, and Business
(1) You might also consider that 1/3+1/3+1/3=1 or .333333...+.33333...+.33333...=1.
Note that we are saying that .99999...=1 exactly, not approximately.
You will encounter other proofs using other ideas as you go through school: the sum of an infinite series, the limit of an infinite sequence, etc...
If you disagree that .99999999....=1, you have some company in the math world, though not much. Look up infinitesimals and you will find a fascinating history of a school of thought that differs from mainstream mathematics.
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calendarEducator since 2010
write133 answers
starTop subjects are Literature, History, and Science
Try this:
0.9999... /= 1
x=0.9999...
10x = 9.9999...
10x-x=9.0...
10x = 9+x = 9.999...
From your line:
10x - x = 9.9999... - 0.9999...
the next line 9x=9 does not follow. It should be
10x = 9.999....
calendarEducator since 2008
write15,967 answers
starTop subjects are Literature, History, and Social Sciences
1 is .99 rounded. The more nines you get, the closer to one you will be. However, 1 will never exactly each 0.99999999, no matter how many nines you add. You will get closer and closer until the differnece is so minimal that you decide to call it 1.
It look like a infinite decimal
so
999999999999999.../1000000000000000...
as
S Infinity=a/1-r
Well... but can you also see it this way?
0.9999... = 1
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999... (becuase x = 0.9999...)
9x = 9
x=1
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