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More Thoughts On Recurring Decimals [May. 15th, 2007|05:29 pm]
Unofficial Murderous Maths Forum on LJ

ummf_on_lj

[yayworthy]
So Chunk was pestering me for a really hard "convert this recurring decimal into a fraction question", so I said ok fine... um... 0.574372924679 and the 9 at the end recurs.

He sat there for a while puzzling and then wondered what 0.000000000009999999... was. I didn't know. [Help much? See below.]

Chunk decided to take an easier version of the problem and go from there and I realised I'd walked him into the 0.9999999.... = 1 idea

He then stumbled upon the proof for this:
0.99999... = n
9.99999... = 10n
9 = 9n
1 = n

So, following this, does 0.000000000009999999... = 0.00000000000.1?

[And on a sidenote, the main irritating thing was once again, McMaffs dismissing non syllabus mathematics, and blatantly NOT GIVING US THE RIGHT ANSWER. She took a look as far as 9 = 9n and concluded that n must be 1/9. >_< GAHCK! What? You call that maths?!?!?]

Briefly accidentally posted to yayworthy. Sorry if you were friendlist spammed at this time.
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Comments:
[User Picture]From: cupati
2007-05-15 05:25 pm (UTC)
If you've counted the zeroes correctly [and remove the stray decimal point], that's right. McMaffs needs educating, but she doesn't sound like the sort of person it is possible to educate.

Also: I get the same fic or set of icons posted to three communities on my friendspage. Accidents don't bother me.
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[User Picture]From: yayworthy
2007-05-15 07:21 pm (UTC)
Coolios. [The zeros were copy and pasted in order to be correct, not sure about the runaway decimal point].

McMaffs... yeah, that sounds about right.

:]
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[User Picture]From: greta_shibuya
2008-11-11 03:40 pm (UTC)
Hmm... I learned in a class 0.999999[..] is 1.0 only when both are real numbers , I remember learning proof of that in Real number theory class. Can't remember the proof the professor used, though, but the one above (or the one bellow) works well if you are not wary of working with technically unknown operations in this case (sum of infitine digit numbers? Can you prove if 0.6666.. + 0.000..1 is 0.6666.. or 0.6666..7?).

1/3 = 0.33333..
3 * (1/3) = 3 * 0.33333..
3/3 = 0.99999..
1 = 0.99999..
(10^-n) * 1 = (10^-n) * 0.99999..
QED

If you use sum of infinite series in the proof, you won't need to deal with the uncertainty of the operations with numbers of infinite digits (or rather, you can use the series sum to prove the operations work fine).
Proving the series are right, though, are other infinite steps. But they do.


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