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#126 Re: Help Me ! » decimal to fraction » 2014-02-17 10:50:31
Hey, get this!!!! I divided seventy-five nine's by 151 and it came out no remainder with wolfram alpha,
so I take this to mean 151 is a factor. Now isn't this something important here we are stumbling upon?
For example if I divide other fractions similar to 89/151 with wolfram, then might I find more factors
that are my denominators for large repeating 99999999-numbers?? Because in this case, wolfram
wasn't displaying prime factors anymore somewhere between 50 and 75 digit numbers, but I
managed to squeeze out the 151 number. Oh well 
I knew there was something here to learn, and
I think that was it right there. Take for example six nines (999999), I predict you can divide that by 7
because 1/7 is repeating on a period of six digits... Wow, and since this is a good tiny find, please
don't move this post up into the other one, it'll just make it more math.
I'm not done baffling you with the math math, because just imagine, what could be done if we
change to hundreds of other number bases!! Now the number that is one less than 100000 or 1000000,
for example, will be not what we now call 999, but in base-7, it would be 343 - 1 or 342. See
what I'm up to??? Fractions in many bases could help aid in finding prime factors of 999 or
Comments always welcome!!
Okay... I filled up a page on my pad of paper doing division in base-4. I divided 156 by 74 or 2130/1022 in base-4.
I got
as usual for fun (math is fun
) (why not guess!? an fix it later) that 4**18 - 1 is divisible by 74, but actually itturns out wolfram alpha says 74/2 is a prime factor and 2 is not since it was odd. Oh well, good first try anyway.
The 3333333333333-method in base-4 might work like the 999999-method in base-10. Any ideas how to
do that one? I'm not up for that division tonight.
#127 Re: Help Me ! » decimal to fraction » 2014-02-17 09:54:20
Thanks bbbm! I forgot about wolfram alpha, haven't used it in a year.
seven 9's = 3 x 3 x 239 x 4649
eight 9's = 3 x 3 x 11 x 73 x 101 x 137
nine 9's = 3 x 3 x 3 x 3 x 37 x 333667
ten 9's = 3 x 3 x 11 x 41 x 271 x 9091
eleven 9's = 3 x 3 x 21649 x 513239
twelve 9's = 3 x 3 x 3 x 7 x 11 x 13 x 37 x 101 x 9901
thirteen 9's = 3 x 3 x 53 x 79 x 265371653
Well, I'm a little disappointed at those huge numbers like 21649 and 265371653, but whatever!?
fifty-nine 9's = 3 x 3 x 2559647034361 x 4340876285657460212144534289928559826755746751
The odd numbers of nines seem to have longer answers, wow I can't believe this 45 digit number
they know is prime: 4340876285657460212144534289928559826755746751
The thing I don't get is like if you take a fraction like say numerator and denominator are between
eighty and two hundred each, then you get these repeating decimals I've been told that are quite long
at for some examples. How is one with this 99999999 method of conversion going to then factor the
fraction into simplest terms. I suppose it must work, but I can't imagine it working with the data above.
Is my brain jumping to conclusions here?? What is your take on this??
Maybe I should try an example with Wolfram like 89/151 and see what I learn...
Well it repeats on a 75 digit period and Wolfram Alpha can go backwards with the following!!! and reduce it!!! wow!!! nice software!!
589403973509933774834437086092715231788079470198675496688741721854304635761/999999999999999999999999999999999999999999999999999999999999999999999999999
and so I tried this out:
999999999999999999999999999999999999999999999999999999999999999999999999999/6622516556291390728476821192052980132450331125827814569536423841059602649 and I got 151!!!!!!
89 times this 6622516556291390728476821192052980132450331125827814569536423841059602649 is the 589403....numerator or repeating part.
So let's see if I learned anything.... I divided 89 by 151 and got a 75 repeating period decimal starting with 58940397....35761 as shown above. Then I divided that 75 digit number with Wolfram by 75 nine's and I got my fraction back, that was startling that wolfram knew that, but when I entered 75 nines into wolfram alpha, it was too long to give me all the prime factors for whatever reason. So next I divided the 75 period number 5894....761 by 89 just to see if Wolfram could do anything with it, and low and behold it gave me a 73 digit number shown above starting 66225165...2649 and so I took that and divided 75 nines by that number and I got my 151 exactly back!!!!!
Welp. That sure was a confusing little experiment. I don't really know what to say.... Anyone have any comments on this???
#128 Re: Help Me ! » decimal to fraction » 2014-02-17 09:15:22
Along the same lines as repeating decimals. Do you think the 9999 or 999999 or 9999999999 numbers have prime factors that might be somehow interesting because we know that certain fractions like 3/7 repeats in fewer than 7 digits?
Info I found so far. 999 x 1001 = 999999
9 = 3 x 3
99 = 3 x 3 x 11
999 = 37 x 3 x 3 x 3
9999 = 99 x 101 = 3 x 3 x 11 x 101
99999 = 271 x 41 x 3 x 3
999999 = 999 x 1001 = (37 x 3 x 3 x 3) x (7 x 11 x 13)
9999999 = Help me??
Can anyone help do more longer ones of these??? (any source welcome!)
#129 Re: Help Me ! » decimal to fraction » 2014-02-17 08:33:41
thank you very much! You beat me to it! I just got to 26/99 = 0.262626262626(26...), so thanks a bunch.
I don't have a use for it today, but I was watching Norman Wildberger doing math on youtube and he mentioned it could be done and in college I had seen the 9999 trick used once in a lecture, but had forgotten the details.
#130 Help Me ! » decimal to fraction » 2014-02-17 08:02:03
- John E. Franklin
- Replies: 8
Given the following number: 11.12346879264332643326433264332643326433(26433...)
Can someone help me convert this to a fraction with the numerator and denominator both counting numbers?
Any hints welcome?
Or a complete exercise would be awesome too.
I haven't looked into it yet, so maybe you can beat me to it, otherwise I'll start researching soon...
#132 Re: Help Me ! » four color cube » 2014-02-15 13:52:19
I spent a couple days drawing this out on a pad of paper and then I entered it into the computer.
It is relative-colors, 1 to 4 colors on the corners of a simple cube or icecube shape.
The use of this is unknown.
#133 Re: Dark Discussions at Cafe Infinity » Happy Valentine's Day » 2014-02-14 06:14:55
Happy Valentines!! My mom made some heart shaped cookies with pink filling!!
#134 Re: Dark Discussions at Cafe Infinity » Moon sightings » 2014-02-13 08:29:55
Wow, that's neat.
So I guess even Mars wouldn't get totally eclipsed by Earth because of the proportions.
That's cool you visited the eclipse. I've seen two eclipes of the sun I remember well.
One I went under a small tree along a road and the crescent shapes of light were
thousands in number under the tree's shadow! Another time I used many polarized
lenses at various turning angles to black out and look for a second at it.
#135 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-13 03:41:04
2712 = 24 x 113
2736 = 24 x 114 = 24 x 2 x 57 = 24 x 2 x 3 x 19
2760 = 24 x 115 = 24 x 23 x 5
#136 Re: Dark Discussions at Cafe Infinity » Moon sightings » 2014-02-13 03:36:43
thanks you for the complete explanation. I understand opposition now. Has there ever in the history of time been an eclipse of Earth against another outer planet? Probably not and the sun is so big you might not get an eclipse anyway.
#137 Re: Dark Discussions at Cafe Infinity » Moon sightings » 2014-02-12 04:20:51
Yes, I have some good binoculars and also a small telescope. I will check soon if I can see 1, 2, 3, or 4 of the Galilean moons with the small red telescope my late uncle got us when I was little. Is the opposition word opposite the Earth thru the sun or elseword?
#138 Re: Dark Discussions at Cafe Infinity » Moon sightings » 2014-02-11 12:36:40
7:15PM EST, the moon was about 7/8 full and the unknown Jupiter planet seems to be about 10 moon diameters NW from the moon. Tonight is tuesday in the 8th week of winter 2014.
#139 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-11 08:26:24
2640 = 24 x 110 = 24 x 11 x 2 x 5
2664 = 24 x 111 = 24 x 37 x 3 = 888 x 3
2688 = 24 x 112 = 24 x 2 x 56 = 24 x 2 x 7 x (2**3) = 2**7 x 3 x 7 = 128 x 21
#140 Re: Dark Discussions at Cafe Infinity » Moon sightings » 2014-02-10 12:46:52
5:49PM EST, the moon was about 3/4 full or 2/3 or thereabout and a planet I think like Jupiter was about 5 moon diameters to the north of the moon. Tonight was Monday in the 8th week of winter 2014.
#141 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-10 12:43:13
2616 = 24 x 109
#142 Re: Help Me ! » four color cube » 2014-02-10 08:43:41
Following from post#3, I have changed the order of the 22 shapes
so that many letters of the alphabet remind me of the shapes, for
example the Q, the R, the M, the N, the I, the braille letter F and braille C.
And it's nice that V and A are upside-down of each other with a not sign in the A.
So here is the next drawing I will build upon later, some in my head.
#143 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-10 03:50:14
2592 = 24 x 108 = 24 x (81 + 27) = 24 x (3**4 + 3**3) = 24 x 27 x 4 = 24 x 27(3 + 1)
#144 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-10 02:37:55
2520 = 24 x 105 = 24 x 21 = 24 x 7 x 3
2544 = 24 x 106 = 24 x 53 x 2
2568 = 24 x 107
#145 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-09 08:36:45
2472 = 24 x 103
2496 = 24 x 104 = 24 x 2 x 52 = 24 x 13 x 8
#146 Re: Puzzles and Games » Add 13 more and post it forever. » 2014-02-09 07:08:00
25636 = 13 x 1972 = 13 x 2 x 986 = 13 x 4 x 493
#147 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-09 02:14:06
2424 = 24 x 101
2448 = 24 x 102
#148 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-06 13:48:54
2352 = 24 x 98 = 24 x 49 x 2
2376 = 24 x 99 = 24 x 33 x 3
2400 = 24 x 100 = 24 x 25 x 4
#149 Re: Puzzles and Games » Add 13 more and post it forever. » 2014-02-06 13:39:05
25610 = 13 x 1970 = 13 x 2 x 5 x 197
#150 Re: Puzzles and Games » Add 24 more and post it forever » 2014-02-06 12:33:22
2184 = 24 x 91 = 24 x 7 x 13
2208 = 24 x 92 = 24 x 23 x 4
2232 = 24 x 93 = 24 x 31 x 3
2256 = 24 x 94 = 24 x 47 x 2
2280 = 24 x 95 = 24 x 19 x 5
2304 = 24 x 96 = 24 x 32 x 3
2328 = 24 x 97