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CTK Exchange
Simon
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Sep-06-02, 08:07 AM (EST) |
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1. "RE: math"
In response to message #0
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Any reccuring decimal is a rational number. To convert to a fraction simply put the reccuring number over as many nines as it has digits e.g. 0.333333 = 3/9
and 0.248248248248... = 248/999 Therefore:
0.99999... = 9/9 = 1 For an interesting demonstration of this, try doing 4/9 by long division then multiplying by 9 by long multiplication. You'd think it would give 4, since (4/9)*4 = 4 |
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jman_red
Member since Jul-2-02
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Sep-06-02, 10:20 PM (EST) |
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2. "RE: math"
In response to message #1
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A small mistake in your math, Simon, (4/9)*4 = 16/9. I think you meant to imply that 4/9 * 9 = 4, which would prove your point. Nikhil, a proof of .9999... = 1. It is on cuttheknot somewhere but i am not sure where. x = .99999...
10x = 9.9999...
10x - x = 9.999... - .999...
9x = 9
x = 1 jman_red |
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RicBrad
Member since Nov-16-01
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Oct-16-02, 07:30 PM (EST) |
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4. "RE: math"
In response to message #3
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>then what will be the value of (0.999999...)^2 ? the same as 1^2, the same as "one"^2, the same as (4/4)^2, etc... >(0.9999999...) must differ from 1 in someways Why? 1 and 0.99999... are different names for the same number. The number given by these two decimal representations is exactly the same. Always remember that things like this are definitions, given meaning only by people, not inherently meaningful. Rich |
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Whymme
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Nov-14-02, 08:00 PM (EST) |
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5. "RE: math"
In response to message #0
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Another proof: Divide 0,9999999...... by three. The result is 0,33333.... People generally know that this is the way in which 1/3 is written. So 0,9999..../3 is the same as 1/3. And another. Subtract 0,999999 from 1. The result is an endless number of zeroes - hence, zero. Therefore, there is no difference between 0,9999999...... and 1. The one mentioned above is the most elegant, though. Whymme |
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