I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857... Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion? Jim Propp
well, 1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769 2307 … although this doesn’t quite break up the repetend 076923. You could use the clumsier 1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 + 0.0000109… = 0.076923… but this involves a bunch of carrying. Cris
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com> wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Hello, we can remark that 142857 is symmetrical, 142 + 857 = 999 so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too. this phenomena is true whenever p <> 2 or p <> 11 and the period is even. best regards, Simon Plouffe Le 2018-03-17 à 21:59, Cris Moore a écrit :
well,
1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769 2307 …
although this doesn’t quite break up the repetend 076923. You could use the clumsier
1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 + 0.0000109… = 0.076923…
but this involves a bunch of carrying.
Cris
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com> wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <simon.plouffe@gmail.com> wrote:
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
nice - since 7 and 13 are both divisors of 1001.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
wait - why does that imply that p divides 10^k+1 for some k? that’s the same as saying that 10 mod p has even order in the multiplicative group, right? Huh... - Cris
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too. - Cris
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
best regards, Simon Plouffe
Le 2018-03-17 à 21:59, Cris Moore a écrit :
well,
1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769 2307 …
although this doesn’t quite break up the repetend 076923. You could use the clumsier
1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 + 0.0000109… = 0.076923…
but this involves a bunch of carrying.
Cris
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com> wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
i like the decimal expansion of 1/9801 On Sat, Mar 17, 2018 at 2:59 PM, Cris Moore <moore@santafe.edu> wrote:
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too.
- Cris
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
best regards, Simon Plouffe
Le 2018-03-17 à 21:59, Cris Moore a écrit :
well,
1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769 2307 …
although this doesn’t quite break up the repetend 076923. You could use the clumsier
1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 + 0.0000109… = 0.076923…
but this involves a bunch of carrying.
Cris
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com> wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
What do you think of 1/9899? On Sun, Mar 18, 2018 at 2:26 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
i like the decimal expansion of 1/9801
On Sat, Mar 17, 2018 at 2:59 PM, Cris Moore <moore@santafe.edu> wrote:
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too.
- Cris
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
best regards, Simon Plouffe
Le 2018-03-17 à 21:59, Cris Moore a écrit :
well,
1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769 2307
…
although this doesn’t quite break up the repetend 076923. You could
use the clumsier
1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 +
0.0000109… = 0.076923…
but this involves a bunch of carrying.
Cris
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com>
wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 =
14/(100-2)
= .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Looks nicely fiby up till 90. (re: Allan Wechsler's 1/9899). On Sun, Mar 18, 2018 at 12:42 PM, Allan Wechsler <acwacw@gmail.com> wrote:
What do you think of 1/9899?
On Sun, Mar 18, 2018 at 2:26 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
i like the decimal expansion of 1/9801
On Sat, Mar 17, 2018 at 2:59 PM, Cris Moore <moore@santafe.edu> wrote:
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too.
- Cris
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <simon.plouffe@gmail.com> wrote:
Hello,
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
best regards, Simon Plouffe
Le 2018-03-17 à 21:59, Cris Moore a écrit :
well,
1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769
2307 …
although this doesn’t quite break up the repetend 076923. You could
use the clumsier
1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 +
0.0000109… = 0.076923…
but this involves a bunch of carrying.
Cris
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com>
wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 =
14/(100-2)
= .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
It’s nice to 89, in addition to being 10^2-10-1, is also a Fibonacci number. How many Fibonacci numbers are of the form n^2-n-1? Jim Propp On Monday, March 19, 2018, James Buddenhagen <jbuddenh@gmail.com> wrote:
Looks nicely fiby up till 90. (re: Allan Wechsler's 1/9899).
On Sun, Mar 18, 2018 at 12:42 PM, Allan Wechsler <acwacw@gmail.com> wrote:
What do you think of 1/9899?
On Sun, Mar 18, 2018 at 2:26 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
i like the decimal expansion of 1/9801
On Sat, Mar 17, 2018 at 2:59 PM, Cris Moore <moore@santafe.edu> wrote:
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too.
- Cris
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <
simon.plouffe@gmail.com>
wrote:
Hello,
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
best regards, Simon Plouffe
Le 2018-03-17 à 21:59, Cris Moore a écrit :
well,
1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769
2307 …
although this doesn’t quite break up the repetend 076923. You
could use the clumsier
1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 +
0.0000109… = 0.076923…
but this involves a bunch of carrying.
Cris
> On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com>
wrote:
> > I just figured out for myself a probably well-known trick for > deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) > = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857... > > > Are there other examples where the repetend of the decimal expansion of 1/n > in splits into blocks that are related to this sort of fashion? > > > Jim Propp > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If you want it to go further, look at 1/998999. On Mon, Mar 19, 2018 at 11:35 AM, James Propp <jamespropp@gmail.com> wrote:
It’s nice to 89, in addition to being 10^2-10-1, is also a Fibonacci number.
How many Fibonacci numbers are of the form n^2-n-1?
Jim Propp
On Monday, March 19, 2018, James Buddenhagen <jbuddenh@gmail.com> wrote:
Looks nicely fiby up till 90. (re: Allan Wechsler's 1/9899).
On Sun, Mar 18, 2018 at 12:42 PM, Allan Wechsler <acwacw@gmail.com> wrote:
What do you think of 1/9899?
On Sun, Mar 18, 2018 at 2:26 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
i like the decimal expansion of 1/9801
On Sat, Mar 17, 2018 at 2:59 PM, Cris Moore <moore@santafe.edu> wrote:
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too.
- Cris
On Mar 17, 2018, at 3:13 PM, Simon Plouffe <
simon.plouffe@gmail.com>
wrote:
Hello,
we can remark that 142857 is symmetrical, 142 + 857 = 999
so one just has to remember half of the period in order to know all of the digits, 1/13 = 076923 , 076+923 = 999 too.
this phenomena is true whenever p <> 2 or p <> 11 and the period is even.
best regards, Simon Plouffe
Le 2018-03-17 à 21:59, Cris Moore a écrit : > well, > > 1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769
2307 …
> > although this doesn’t quite break up the repetend 076923. You could use the clumsier > > 1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 + 0.0000109… = 0.076923… > > but this involves a bunch of carrying. > > Cris > >> On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com
wrote:
>> >> I just figured out for myself a probably well-known trick for >> deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) >> = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857... >> >> >> Are there other examples where the repetend of the decimal expansion of 1/n >> in splits into blocks that are related to this sort of fashion? >> >> >> Jim Propp >> _______________________________________________ >> math-fun mailing list >> math-fun@mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
1/499 is good too. On Mon, Mar 19, 2018 at 11:44 AM, Allan Wechsler <acwacw@gmail.com> wrote:
If you want it to go further, look at 1/998999.
On Mon, Mar 19, 2018 at 11:35 AM, James Propp <jamespropp@gmail.com> wrote:
It’s nice to 89, in addition to being 10^2-10-1, is also a Fibonacci number.
How many Fibonacci numbers are of the form n^2-n-1?
Jim Propp
On Monday, March 19, 2018, James Buddenhagen <jbuddenh@gmail.com> wrote:
Looks nicely fiby up till 90. (re: Allan Wechsler's 1/9899).
On Sun, Mar 18, 2018 at 12:42 PM, Allan Wechsler <acwacw@gmail.com> wrote:
What do you think of 1/9899?
On Sun, Mar 18, 2018 at 2:26 PM, Thane Plambeck <tplambeck@gmail.com> wrote:
i like the decimal expansion of 1/9801
On Sat, Mar 17, 2018 at 2:59 PM, Cris Moore <moore@santafe.edu> wrote:
Indeed, 14+28+57 = 99… because 7 is a divisor of 10101... and 07+69+23 = 99, because 13 is too.
- Cris
> On Mar 17, 2018, at 3:13 PM, Simon Plouffe <
simon.plouffe@gmail.com>
wrote: > > > > Hello, > > we can remark that 142857 is symmetrical, 142 + 857 = 999 > > so one just has to remember half of the period in order to > know all of the digits, > 1/13 = 076923 , 076+923 = 999 too. > > this phenomena is true whenever p <> 2 or p <> 11 and > the period is even. > > best regards, > Simon Plouffe > > > Le 2018-03-17 à 21:59, Cris Moore a écrit : >> well, >> >> 1/13 = 0769/9997 = 0.0769 (1 + 0.0003 + 0.00000009 + …) = 0.0769 2307 … >> >> although this doesn’t quite break up the repetend 076923. You could use the clumsier >> >> 1/13 = 076/988 = 0.076 (1 + 0.012 + 0.000144) = 0.076 + 0.000912 + 0.0000109… = 0.076923… >> >> but this involves a bunch of carrying. >> >> Cris >> >>> On Mar 17, 2018, at 2:36 PM, James Propp < jamespropp@gmail.com> wrote: >>> >>> I just figured out for myself a probably well-known trick for >>> deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) >>> = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857... >>> >>> >>> Are there other examples where the repetend of the decimal expansion of 1/n >>> in splits into blocks that are related to this sort of fashion? >>> >>> >>> Jim Propp >>> _______________________________________________ >>> math-fun mailing list >>> math-fun@mailman.xmission.com >>> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-f un >> >> _______________________________________________ >> math-fun mailing list >> math-fun@mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > _______________________________________________ > math-fun mailing list > math-fun@mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/ _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Of course, short repetends happen whenever the denominator is a factor of 10^k-1: 1/11 = 9/99 = 0.09 09 09... 1/37 = 27/999 = 0.027 027 027… 1/101 = 99/9999 = 0.0099 0099… 1/41 = 2439/99999 = 0.02439 02439 1/271 = 369/99999 = 0.00369 00369… 1/13 = 76923/999999 = 0.076923 076923… I remember being fascinated by these when I was a kid.
On Mar 17, 2018, at 2:36 PM, James Propp <jamespropp@gmail.com> wrote:
I just figured out for myself a probably well-known trick for deriving/remembering the decimal expansion of 1/7: 1/7 = 14/98 = 14/(100-2) = .14/(1-.02) = .14 + .0028 + .000056 + .00000112 + ... = .142857...
Are there other examples where the repetend of the decimal expansion of 1/n in splits into blocks that are related to this sort of fashion?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (6)
-
Allan Wechsler -
Cris Moore -
James Buddenhagen -
James Propp -
Simon Plouffe -
Thane Plambeck