0.99999 = 1
posted by Rajesh Lal at
1:04 PM
Thursday, March 5, 2009
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15 Comments:
When you are rounding
This can be clearly proven in several ways, two ways I will demonstrate: (.333-> means .33333333333 (infinite 3s))
Method 1:
1/3 = .333...
1/3 + 1/3 + 1/3 = .333-> + .333-> + .333->
1 = .999->
Method 2:
k = .999->
10k = 9.999-> (multiply both side by 10)
10k = 9.999->
- k = .999
---------------- (subtract one equation from the other.)
9k = 9
k = 1
Both of these methods prove that 0.999-> = 1. That is EXACTLY EQUAL.
lim (x) = 1
x - 1
okay.
Those commments above isn't incorrect.
But 0.9999.... does not exactly equal 1.
It is assumed just like 1/infiny=0.
This is what mathmaticians call a limit.
0.9999....=lim1,
1/infinity=lim0.
But we see it as 0.999..=1, 1/infinity=0.
So if we see 1/infinity=0,
then we can come up with this:
0.999999....=1-0.000....001.
Right?
and since 1/infinity=0.000....001=lim0=0, then 1-0=1.
So therefore 0.999...=1
0.99999... = 0.9 + 0.1 * 0.9 + (0.1)^2 * 0.9 + ...
which is a geometric series with a common ratio of 0.1, and a first term of 0.9
so, the value of that sum is:
0.9 / (1 - 0.1) = 0.9 / 0.9 = 1
0.99999 can equal 1
when it's approporate.
It's approporate when you are talking about money.
It's not approporate when you are figuring something that needs accuracy more than 4 decimal places.
Genearally 2 places are ok, so most of the time they are equal.
take the absolute value of .99999 which equals one.
raise to the power zero
it doesn't matter how you try to dress it up with fancy mathematics, it never equals 1.
Only if you round to the nearest whole number
its very simple. When your mom give u 100buks to buy 90buks..do u return 10buks..or will u roundoff it to 100????
LOL...
i love lamp
the answer is 3/3 as demonstrated
1/3= .333333..............
2/3= .666666.............
3/3= .999999..........
or 1 XD
I LIEK MUDKIPZ
In mathematics 0.99999 (repeating) always equals 1, ask any math teacher. That is just a fact.
1/3 = 0.3333 (repeating)
3 * 1/3 = 1
3 * 0.333 = 0.999 (repeating)
thus, 1 = 0.999 (repeating)
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