998,001 and its Mysterious Recurring Decimals - Numberphile

There has been some internet buzz about 998001, so Numberphile sheds some light on matters.
More links & stuff in full description below ↓↓↓
This video features Dr James Grime and we mention the KZbin channel Vsauce.
James' website: singingbanana.com/
Vsauce: / vsauce
Blog on the brown paper issue: periodicvideos.blogspot.com/20...
NUMBERPHILE
Website: www.numberphile.com/
Numberphile on Facebook: / numberphile
Numberphile tweets: / numberphile
Subscribe: bit.ly/Numberphile_Sub
Videos by Brady Haran
Patreon: / numberphile
Brady's videos subreddit: / bradyharan
Brady's latest videos across all channels: www.bradyharanblog.com/
Sign up for (occasional) emails: eepurl.com/YdjL9
Numberphile T-Shirts: teespring.com/stores/numberphile
Other merchandise: store.dftba.com/collections/n...

[@suimarc]

He seems to be the happiest person alive

[@Youtube_Globetrotter]

+DASMARC You can count on that, or maybe he can......

[@Oryon44]

He really looks like he does these videos with passion for math, he looks like he was born for math and he's so happy that he went for math in his life.

[@iholc]

+Oryon *meth

[@ImSquiggs]

+DASMARC I really dig this guy. I'm just starting to watch these videos but his excitement gets me into it, and I usually hate math, haha.

[@ridzwannafiz4073]

look at this guy

[@SUNDOWNER88]

nein, nein, nein, nein, ..., nein

[@HitlerRants]

+Bahadır Onur Güdürü im here

[@emirhan5781]

Lol

[@haferman92]

Plüschi he was saying that as i read i lol

[@jonwicks9473]

Hans....

[@DrCartouche]

Was about to upvote, but the fact that the comment is 999 makes me want to let this pleasure to someone else

[@thisisblackmesa]

who else cries themselves to sleep

[@WalterKingstone]

+Molun I know right

[@bantaar]

+Molun Another way to look at it also gives me some peace. Consider the simpler example of 1/81 = 1/(9*9) . If you do it in two steps, first dividing 1 by 9, you get 0.1111111.... Not at all odd, when you look at the pattern emerging by normal division. You divide 10 by 9 in each step, and get the REMAINDER 1. Which is why you'll have 10 to divide in the next step. Then, to get to the final result, you divide the endless row of 1's by 9. Now your first step yielding something non-zero, you'll be dividing 11 by 9, getting remainder 2. Next step, 21/9 leaves remainder 3. See the pattern? Yup, you get ...4,5,6,7, in the remainders. So why no digit 8 in the sequence. Because after the remainder 8, you'll be dividing 81 by 9, so you suddenly no longer have a remainder, and so the sequence starts over.

[@bantaar]

+Molun By the way, following my previous comment, I get a suspicion of what's going on. Could it be that te reason that I get the neat sequence, is that 9 is the smoking gun here? It's special in the way that it's the highest single-digit number in the decimal system. Boy... I have to go now. I must make some calculation... say, in base 12, and using 11 (which will be the highest single-digit number there)...

[@MultiJman01]

I really want to like the comment but I can't (look at the likes).

[@kisaragiayami]

Satis-fraction plz plz

[@vimalsobhee]

10 (the director): "Hey 9, keep that one for me" 9 (the manager): "Hey 8, keep that one for me" 8(the trainee): "okay"

[@notlsa]

brilliant

[@ThinkAboutVic]

@@notlsa hello notlsa geometry dash

[@jwcfive7999]

@@notlsa hello notlsa geometry dash

[@rafiihsanalfathin9479]

@@notlsa hello notlsa geometry dash

[@splenden2235]

@@notlsa hello notlsa geometry dash

[@josephvictory9536]

So your saying that 7 didn't ate 9 my life is a lie

[@theroskyyyy]

+Marcin Gołda i see what you both did right there too

[@abdumalikmustapha4689]

+Joseph Victor I see what you three did there.

[@luciancrosby6331]

+Abdumalik Mustapha i see what you four did there

[@NoahVN]

+Lucian Crosby I see what you FIVE did there.

[@oliver8500]

+NoahVN I see what you six did there.

[@oddatsea9398]

1÷(101×101)=0.00009802960494069208 It's funny because the number that comes after 9 decreases by 2 while the number infront of nine increase by 2. Weird

[@haze13_]

cool

[@demonetizeddemonetisedinmy1890]

lies

[@houkouha4427]

that name........

[@RobbyBoy167]

+Filip, hover above that name and read what the pop up says. hahaha this dude!!

[@hugoperhammer]

Not only that. Even two digit numbers decending from 98 and ascending from 02 (9802 9604 9406 9208 9010 8812 8614) all the way to 0298. Then starting at 0099 doing the reverse with odd numbers 9901 9703 back to 0000 and then repeating every 400 digits.

[@thefleepo8013]

"Six, seven... Skip a few Then we've got 996"

[@yoursleepparalysisdemon1828]

How Why

[@billymatthews4150]

Searched for this exact comment

[@rowenagarcia6088]

@ The Fleepo | Hey, they just said that because doing the whole thing would be VERY BORING. So they intended that to be *fast forward until*.

[@joegillian314]

Considering that 1/9 itself is an infinite decimal expansion of 1's, it makes sense that dividing by a number consisting of a string of 9's would end up creating another infinite decimal.

[@yaboi7034]

At least at the beginning.

[@IAMASTICKSTUPIDPERSON]

@@yaboi7034 are you sure about taht

[@ethankremer5694]

If you call '0000000' repeating decimal (understand if you don't) then technically every rational number will end in a repeating decimal, especially since if you check the numbers in a different base it might not be 000000

[@MegaBitmap]

0:55 Lol skip a few: 007...996

[@CheyenneAnastacia]

IM LAUGHING SO HARD 😂😂😂😂😂 and this is like years ago 😂😂😂😂😂😂

[@Henrique.tRo_Real]

"""""a few"""""

[@altrogeruvah]

This reminds me of a little math trick my private math teacher used to show me decades ago: 12345679 x 54 = 66666666... 12345679 x 63 = 77777777... 12345679 x 72 = 88888888... ...and so forth. Works backwards as well. (45, 36, 27, you probably understand this pattern by now) You basically omit the 8 and follow this adding pattern. I don't know whether that's a popular trick or not, but I thought it was cool!

[@GeonQuuin]

it is cool. At least I think it is.

[@rgqwerty63]

I remember finding that really cool when I was younger, but know you can kind of see why which makes it less interesting 12345679 *9a = 1111111111*a and you can easily see that makes the repeated "a"

[@dotXyore]

rgqwerty63 Still a neat little algorithm.

[@nyannc]

6666666606... *

[@crackedemerald4930]

Why is 8 excluded?

[@jazzybank]

5:21 "That you will learn at some point" *Learns in the video.*

[@ayamrudin7985]

lol

[@ick567]

Lol

[@ick567]

1/998001

[@samueldeandrade8535]

Pretty easy formula ...

[@chaosPneumatic]

I got 998,001 problems but a terminating decimal ain't one. Hit me!

[@sandmangaming1790]

you were adopted

[@losthor1zon]

But you do repeat yourself.

[@tristanwillstout658]

*_*Falcon PUNCH™*_* yeah that's right noobs I trademarked it hahahahahaha

[@xit1254]

Fascinating explanation! Years ago, when HP came out with the first scientific calculators, I found something similar while playing on my new HP35. It gives the powers of 2: 1/49, 1/499, 1/4999, etc.

[@samueldeandrade8535]

Oh my Euler! Your comment is even more interesting than the thing in the video!

[@eddyji999]

why am i watching this on a friday night?

[@N00byEdge]

That would be a Sunday, time zones might make that a Sunday or a Monday, according to publishing date I am seeing. A Friday is not possible.

[@TheFekke100]

Because you're awesome! :)

[@mikhailman]

coz you're smarter then those spending their night in a night club vomiting.

[@dotFrazUnderscore]

we're all nerds, so we don't have anything else to do

[@TheMvinas5]

i'm watching this on a saturday night

[@ffggddss]

Nicely done! Another fun thing to try, that's related, is x/(1-x-x²) = F₀x⁰ + F₁x + F₂x² + F₃x³ + ... where Fᵢ is the i'th Fibonacci number. If x is taken as a positive integer power of 0.1, say, 1/10ⁿ, you get Fibonacci numbers until they 'bump into' one another by having more than n digits. Also, what you've shown, is a way to get a counting sequence; the sequence of positive integers, with that 'jump' near the end. You can carry it another step, and get the sequence of triangular numbers by cubing, instead of squaring, the n-9's denominator. So 1/999³ = 1/997002999 = .000 000 001 003 006 010 015 021 ... And with a 4th power in the denominator, you get the pyramidal numbers, and so on...

[@tim..indeed]

>My satisfaction when I actually understand why the 8 is missing

[@chevtothemax]

Tim Fischer I love that the answer is literally the trope of 'carry the #'

[@gothenix]

My satisfaction when I see Asterix

[@r390gt1lm]

he is the happiest nerd I have seen lol

[@Manysdugjohn]

Nerd is someone that values things that have no real life value. Like Video gamers. You can't call some1 nerd because he is a mathematician.

[@r390gt1lm]

if I want to know that, i google it

[@SrNkolaidis]

John Milionis define life value

[@Penguin-kr9do]

John Milionis Video games have no real life value? Actually, they do have one. It's called "fun".

[@r390gt1lm]

Penguin236 yea, its like saying that movies, books and music have no value

[@JohnOlly1965]

Something else about the number 9 as well. If you add up all the digits in a number and that number can be divided by 9 then the bigger number can also be divided by 9. Example: 7011 >> 7 + 0 + 1 + 1 = 9 Proves you can divide 7011 by 9 = 779 Example.2) 52017102 5+2+0+1+7+1+0+2 = 18 then 1 + 8 = 9 Proof 52017102 / 9 = 5779678 The bigger number can be as long as you like. :-)

[@benhudelson]

🎼 Carry on my eighth spot sum. You'll be nine when we are done. 🎼

[@trequor]

Ben Hudelson underrated

[@jayfredrickson8632]

LOL

[@Hopesedge]

I like that 111,111,111 x 111,111,111 = 12,345,678,987,654,321. It's a simple one but it's still neat.

[@tommychan7170]

+Hopesedge There was a thing called OTTO numbers but after a counter example was found such as 111111111111x111111111111 it was trashed

[@Hopesedge]

tommy chan Interesting, I had no idea. Thanks for the free knowledge!

[@tommychan7170]

+Hopesedge Thank you for appreciating it :-D

[@javieraracil782]

+Hopesedge 98,765-43,210= 55,555 and 43,210+56,789= 99,999

[@obaidadaraghmeh9303]

1+1=2

[@funicio]

Holy cow!

[@alejandromatosanguis5267]

Edwin Camuy And 2-1=1

[@funicio]

Alejandro Matos Anguis Dude!

[@RedHairdo]

Obaida Daraghmeh loominarty

[@szlomajosif2711]

RedHairdo And one minus one is not at all :)

[@nakedking6676]

NEIN NEIN NEIN NEIN NEIN...

[@roridev]

NEIN!

[@jalilcompaore]

NakedKing NEIINNN! Ne in nei nne inneinnei nnei nneinnein nei n !

[@jamesjacocks6221]

Cute!

[@roridev]

James Jacocks NAIN!

[@AaronHollander314]

that escalated quickly

[@Aazel]

4:46 And then he became German

[@Rosharnus]

Nein! Nein! Nein! Nein! Nein! Nein! Nein! Nein! Nein!

[@iamwhatitorture6072]

Doch! Doch! Doch! Doch! Doch! Doch! Doch! Doch! Doch! Doch!

[@Xnoob545]

When riddle says .999999999999 whatewer amount of nines 51% the speed of light

[@tanzimahmed3860]

Dear Numberphile, get a whiteboard Best of regards, YT viewers

[@numberphile]

one viewer! some people love the brown paper!

[@tanzimahmed3860]

+Numberphile aw C'mon :D

[@khudhurghazi2937]

+Tanzim Ahmed i love the brown paper

[@miguelschwarzbold2219]

#BrownPaperTheBest

[@FourthDerivative]

Brown paper 4 lyfe

[@moelr_]

4:45 "NEIN NEIN NEIN NEIN NEIN NEIN!!!!"

[@DominikLederhas]

"Let's get you more paper."

[@MistahPhone]

3:30

[@timothytraver5918]

Get this man his brown paper, stat!

[@DARKSN0VV]

Pingu's lost cousin right there 0:28

[@jaredcarter1165]

i know they love their brown paper, but seriously unless they're storing them like manuscripts after using them, why not dry erase board?

[@krmunoz2169]

+jared carter I think they do store them and sell them online if you're a fan.

[@Szgerle]

Chemicals are used in the production of every paper.

[@cooperfoster4645]

THEY'RE THE SACRED TEXTS

[@brcoutme]

The paper is brown because it is recycled paper, and paper is made of a renewable resource. Aren't you being a bit picky here? I mean I understand that we use more paper than might be renewable in terms of tree growth right now, but still it is recycled paper anyways.

[@watcherofwatchers]

Also, dry erase boards are terrible.

[@saboo_tage]

NOOT NOOT since when did you turn into pingu?

[@GummieI]

+Xyko Yeah i always found the way he says 0 weird

[@gizmodude7885]

They're British.

[@TheMrYakobo]

But he alternates between saying zero and naught at 6:52

[@Skiddla]

knought, hes reptilian

[@mysillyusername]

I do that too, but it's well weird.

[@Bonmoustache]

that awkward moment when he starts speaking german 4:45

[@sylasviper715]

It's English. 9 != nein

[@Bonmoustache]

you know I was kidding, right? it's important to me that you know that

[@MrManlify]

+Prerendered renderation No 9! = 362,880

[@cg9887]

+Aamir Quraishy != means not equal to LÖL

[@prakhar9998]

+0 you must be fun at parties

[@bowel_movement]

What a great video! Everything explained was so interesting. The whole time I was wondering, why the 8? Really cool that you saved that one for the end :)

[@rodovre]

One of the best in the series, well done! There is a variant I learned at school: You type 12345679 in a calculator, then 'Give me a digit 1..9', say you select 5. 9 times 5 gives you 45. So you look clever and then multiply 12345679 with 45, and get all 5's....

[@ThomasHaberkorn]

nein nein nein nein squared

[@sadekausi]

noot noot noot

[@EchoHeo]

Pepijn its naught not not

[@EchoHeo]

Hu huh . not not.

[@tristanwillstout658]

yee

[@gothenix]

Noombah

[@Zeddle]

Noot

[@HeyKevinYT]

4:11 watch your fingers!

[@dikshantraj6005]

This videos is just awesome! Your love for numbers is unmatchable :)

[@dsamh]

noticed this years ago when I accidentally hit the return twice dividing 1/9. Spent a while trying to suss it out and figured it was just another little mystery of the number 9. Nice to see that explained so well. But it is still a little mysterious :P

[@asd49789]

Every episode on this channel is like a rare kind of cigar or some quite classic whiskey, that you can just enjoy while you brood on the interesting facts of life, just having this in your little free time every day. Moreover, this is a rather healthy way of enjoying your moments

[@user-pc8en9lh7u]

I like how that number and repeated decimals have such an elegant explanation. Maths!

[@DepFromDiscord]

Никита Лубин math*

[@aaronleperspicace1704]

@@DepFromDiscord no only americunts say it like that. It's maths.

[@SG2048-meta]

@@DepFromDiscord UK spelling

[@PC_Simo]

@@DepFromDiscord I know ”Math” is older, but someone has to put America back in its place.

[@LeonMire]

That is "nought" how you say zero! :P

[@andyyang3029]

That is "naught" how you spell naught! :P

[@LeonMire]

Is it usually spelled "naught" in the UK? I'd only ever seen it spelled "nought" (which was not that often), and the dictionary has both.

[@andyyang3029]

They're both correct haha. I just saw the opportunity for yet another pun and took it

[@theendofthestart8179]

if you press the caption option on youtube, it spells it "nought"

[@totalsyambles8308]

"Naught" means to ruin, while "nought" is a circle.

[@tressino343]

I always hated math class and never felt like I learned anything no matter how hard I tried, but watching someone this enthusiastic about math and numbers actually make me want to learn more. I never had a teacher that made math engaging, here I feel like I am actually learning.

[@michailbialkovicz878]

0.9999... Repeating number is 9, so 0.999...= 9/9 = 1 right?

[@AndrewRollette]

No, not at all. do math

[@michailbialkovicz878]

Andrew Rollette Already did, show me what's wrong.

[@goldenayaka]

9/9 is 1. 0.9999999... and so on will never be one.

[@goldenayaka]

Ahh, alright. Thank you for clearing it up for me. Apologies to the OP for saying things wrong.

[@33LB]

Michail Bialkovicz there's nothing wrong. mathematically, 0.999... (recurring) is exactly equal to one.

[@Scholaf_Olz]

This guys enthusiasm made me binge watch Numberphile videos, even though I hated math in school

[@deansprivatearchive]

I immediately came to this video since I've wondered what 999x999 is since I was very little, and now have 998,001 memorized in my head.

[@mrimatt6210]

Great explanation! The missing 8 was particularly cool.

[@dpaek85]

so satisfying to see a logical explanation to something initially presented as a quirky pattern in an arbitrary scenario!

[@VanillaSnake21]

I didn't care too much about the recurring thing or the camera work, but in a few minutes of watching this I finally understood what infinite sets are all about, so I have to say great video

[@VWftw82]

I just thought of a way to think of this: rep-digit numbers with 9s to the negative 2nd power include every number half as long as the answer to that expression except the first half of that square number. I realized it when James pointed at the 998 in 998,001. This sounded super complicated when I was typing it so 81 is missing the 8; 9,801 is missing the 98; etc.

[@JStraight160lbs]

I always thought 7 ate 9 but I guess 10 ate 9

[@needlessToo]

"Nice number". That's a nice expression. Only someone into art of mathematics would say that.

[@bhargawgaikwad2866]

please do it for 1/7 and 7 multiples that's also an interesting mathematical series

[@alexs710]

hey discovered ur channel today, watched like 5-6 vids, everything awesome, the only recurrent unsatisfying thing is that fancy paper u use in all vids with a incredibly bad gestion of it's space :D

[@BrunoBsso]

Another interesting thing happens with 1/997002. Every pack of three decimal digits, including the first one which would be the integer 001, is the double (and this multiplication by two is in fact the difference between 999 and 997, which is two, and is also the value of the last three digits which is 002; same applies to 998001, and so on) of the previous pack plus one. 1,0030070150310631272555120250511 (001 * 2) + 1 = 003 which is the first pack after the comma. (003 * 2) + 1 = 007 which is the second pack. (007 * 2) + 1 = 015 which is the third pack. (015 - 2) + 1 = 031 which is the fourth pack, and so on. With 996003, it results in the same, but multiplying by 3: (1 * 3) + 1 = 004 | (004 * 3) +1 = 013 | (013 * 3) + 1 = 40 | 040... and again. Very interesting stuff indeed, at least for me (I'm not a mathematician at all).

[@BrunoBsso]

And also, the divisor is the one who makes the rules. The X digits packs are directly related to the divisor's lenght divided by 2. A 6 digits long divisor (998001, 997002 ...) generates 3 digits packs in the decimal side (6 / 2 = 3) -> first pack is 002. An 8 digits long divisor (99980001 ...) generates a 4 digits pack in the decimal side (8 / 2 = 4) -> first pack is 0002. It's still awesome :D

[@bethysboutique]

9 is an amazing number!

[@chriskennedy00085]

and 6 too..

[@dewolenyt]

Nein

[@akianaray651]

Giving us the real facts.

[@brcoutme]

Not sure if you feel that way because of the reasons connected to it being the last digit in our base ten (such as in this video). I mean their are other reasons why nine is an amazing number being three squared, it has many neat properties in it's own right.

[@dushyanthabandarapalipana5492]

Thanks !happy new year!

[@gliderfan6196]

I am happy for the internet to make this cool little fact so viral that Dr Grime explains it to me. The amazing fact is just awesome, but knowing the mechanism behind the fact is really cool. I love the pause before he said the word 'formula' like it was something you should not say in a company of ladies. And I could share his excitement when I made a division that ended with 0,31415926

[@jamesjacocks6221]

The brown paper is perfect. Functional and pedestrian. As to why a problem goes viral, we have to consider the nature of fascenation, of lacking some element of understanding and to some degree being outside complete comprehension. Once something (or concept, etc.) is thoroughly understood it becomes ordinary. You might be able to make a simple formula of this, Doctor. Would love to see your uncertainty equation.

[@AvoDJ]

...do you mean "fascination"...

[@jamesjacocks6221]

Yes.

[@EndrChe]

James Jacocks I rather like your spelling though.

[@jamesjacocks6221]

Duh.

[@mistersir5618]

Why...ur not cool

[@Anthony-cn8ll]

If you want to include the 8. 13,717,421 -------- 1,111,111,111

[@MrLol-lt6ib]

Anthony Vanover how did u find that????

[@Anthony-cn8ll]

123,456,789 ----------------- 9,999,999,999 will give us the decimal we're looking for. Now notice they the are both divisible by 9. For the denominator, this is easy to see. It comes out to 1,111,111,111 when divided by 9. The numerator is tricky at first glance, but try counting by 9's above 99. 108, 117, 126, 135, 144, 153, 162, 171, 180, 189. Notice how this sequence is a bit off from when you count by 9's below 99? Instead of 9, 18, 27 we get 8, 17, 26. So every time the ones places goes back to 0, there will be a shift. This pattern is key to why 123,456,789 is divisible by 9. If you divide it by 9 you will get 13,717,421. Interestingly this is almost a prime number, but it actually has two other factors, 3607 and 3803 which are both prime.

[@ffggddss]

Yes, the easiest way to see the divisibility by 9 of the numerator, is by the technique of "digital roots;" that is, the sum of the digits, 1 through 9, is 45, and the sum of *its* digits is 9; so the original number is divisible by 9. Dividing by 9, gives what you've shown, and another digital-root check shows that it is now indivisible by 3. So then it's on to larger prime factors, as you say, which in this case, there are none that divide both terms.

[@Anthony-cn8ll]

ffggddss There's a game called "Nine Hours, Nine Persons, Nine Doors". For anyone that doesn't understand digital roots, try playing this game.

[@GraveUypo]

i was gonna ask if this was a re-upload because i remember seeing it before, then i realized i was not at my subscriptions box, i was at the initial page with all the recommendations. oh well, it was worth watching again.

[@cptechno]

QUESTION: Would there be an advantage to create a number system using a prime base rather than base 10. For example, using base 11 or base 13 instead of base 10, which is not a prime number?

[@MrxstGrssmnstMttckstPhlNelThot]

And if you do 1/FFE001 a similar thing happens in base 16. Does this rule carry on for every base that 1/(b^n-1)^2 where b is the base and n is an arbitrary number gives you a number like this in that base? A little testing with WolframAlpha would seem to indicate yes.

[@groszak1]

And 1/110001 in binary

[@MarioFanGamer659]

Rule of thumb: When ever there is a propertly relatated to 9 in base 10, it mostly likely is also a thing in other bases as b-1.

[@jace427]

I know this is an old video, but can you go through why 1/499 appears to be the powers of 2, in 3 digit increments (i.e. 0.002004008016032...)? I'd love to see why that is true; a little different from sequential digits. It appears to do some overlap after' 064'. Tried it out with additional and reduced number of 9s and all seem to be variations with different significant places like your video here.

[@hypergration_htan]

Maybe you have already figured out the answer by now but here it is anyway:- First, Observe that 1/499 = 2/998 Next, 1/998 = 1 / (1000-2) = 1/1000 * [ 1 / (1 - 2/1000) ] Next, We can convert the term 1 / (1 - 2/1000) into a GP series as 1 + (2/1000) + (2/1000)^2 + (2/1000)^3 + ... = 1 + 0.002 + 0.000004 + 0.000000008 + 0.000000000016 + ... = 1.002004008016032064128256513026..... Finally, 1/998 = 1/1000 * 1.002004008016032064128256513026..... = 0.001002004008016032064128256513026..... Thus, 1/499 = 0.002004008016032064128256513026..... This idea carries over to similar patterns. For instance, 0.003009027081243731.... = 1/997 etc.

[@annazarifopoulou9580]

Vsause and this channel just gives me the chills

[@TechTheHedgehog]

Fun Fact: If you split the denominator of your fraction [your (((10^x)-1)^2)], you get both the missing decimal segment (8, 98, 998, etc.) and and the first "whole" number of the series (1, 01, 001, etc.).

[@kinana6147]

Just wondering: Is there any reason why every time i multiply 625 by itself, i get a number ending in 625? 625*625= 390625 625*625*625= 244140625 625*625*625*625= 152587890625 Is this some profound thing?

[@corymason5541]

I'm not 100% sure of why it is, but it probably has something to do with the fact that 625 = 5^4 or 25^2, and every odd numbered multiple of 5 has 5 at the end of it.

[@kinana6147]

Cory Mason Interesting!

[@boblee0192]

It's about as profound as our solar system having exactly eight planets

[@NitinGrewal]

because it has a pattern. Any power of 5 will end in 5. Any power of 25 will end in 25. Any power of 625 will end in 625. Any Power of 390625 will end in 390625. And the sequence of these numbers is 5, 25, 625, 390625 ...... and so on Alternatively, I should have written as 5^1, 5^2, 5^4, 5^8, 5^16 and so on.

[@Hansondiandian]

Nitin Grewal dude, any odd powers of 390625 will end in 390625; however, any even powers would end in 890625

[@anyname8235]

I saw this number (1/998001) in Arkham Knight in the last Riddler room (Final Exam).

[@mohdasyraafsyahmi3250]

this video's explanation is awesome. thumbs up for you

[@SparkeyGames]

It works in any base. B=base, B-1= your last symbol which is always the “carry on”, so B-2= your skipped number. So, 1 over (Bsq)-1 = repeating places using all symbols in your base except B-2. Try it!

[@-kenik9629]

Hey do you get the same effect if you convert it into hexadecimal?

[@MegaMinerd]

What about 1/7? The decimals contain the first 3 even 2-digit multiples of 7 (14, 28, 42) and 1 more than the second 3 2-digit multiples of 7 (57, 71, 85). Is there a video for that yet?

[@Luffy-yz9gj]

MegaMinerd I see that different:(_ period) 1/7 is 0._142857 right now sort the numbers by their sizes->124578 2/7 will be the same like 1/7 but it starts with the next number (size): 0._285714 The same with 3/7 and....0._428571, 0,_571428, 0,_714285, 0,_857142

[@benji104]

look up cyclic numbers. there is even a wikipedia article about the number 142857. it boilds down to a geometric series and can be done in principle with any fraction, but it looks rather nice with 1/7

[@ricie9317]

The ancient approximation of PI of the Egyptian was 256/81.The result is approximately 3.16. The value 3.16 can be used to test the primality of a number. The method that I discovered using this value can clearly demonstrate the characteristics of prime numbers.

[@masego5217]

It also works in different bases of numbers too. 1/7^2 in base 8 comes out the same as 1/9^2 in base 10 for example

[@mememeet4140]

nein nein nein nein nein 4:45

[@BrendanGuildea]

Downfall!

[@Rick_Sanchez_Jr.]

I didn't understand a single thing that was said but I did poop on myself during the video...

[@GateCrasherVI]

I feel like I could sit down and correlate this to electrical binary logic "memory errors" or maybe the right nomenclature would be something like "buffer over-run". Little bits of data carrying forward until finally it culminates in an error value.

[@ForTomorrowToday]

What eerie is that I think I watched this video years ago in school and I think repeat too just like 998001.

[@aspermwhalespontaneouslyca8938]

ah, yes An, my favourite number.

[@FandangoJepZ]

Didn’t watch this video before now, and I’m happy I didn’t. I worked on this for a 24 hour project for math loving middle schoolers (along with decimal expansion proof, harmonic series and other convergent/divergent series). Decimal expansion proof was the most fascinating one and I got it after 6 hours!

[@BleisermanADN]

One of the most satisfactory things in the video id the fact that the audio is insanely nice even if he is in a classroom

[@walterchavez3081]

Maybe Numberphile can do a show on why when you have a numerator(?),denominator(?),both(?) that is prime P then you generally won't get a repeating decimal pattern until P digits have passed. The repeating decimals often appear quite random, but I don't think they are used in psuedorandom functions so they are probably not random enough and/or there is another problem.(maybe I'm the first one to come up with the idea!!!!)

[@mymicrowave]

I really like numberphile, I hope it sparks others interest in maths as much as it does mine.

[@Bob-gc9gd]

4:44 "Nine over 11" i r8 9/999999999 m8

[@veme2857]

Wow, very interesting. Keep going making videos :)

[@BartoszMotyka]

another weird thing(for me) is how 999^2=998001 and 333^2=110889... i mean think about it. 998001 | 110889. And also, another cool thing is that when u let's reduce 3s so lets say instead of 333^2 u do 33^2, the result is very similar 1089, so basically you just remove the 2 numbers that were in the middle. Now, when u add a few 3s, so for instance you have 33333^2 you get 1111088889. So it's always adding 0s and 8s in the middle. the same works for 99^2, 999^2, 9999^2 etc (and also 66^2, 666^2, 6666^2 etc).

[@saultube44]

People are starting to use their brains and realizing how interesting, interesting science facts are.

[@saultube44]

Brendan Matthews I don't like your derogatory attitude. use your braina dn realize that some poeople not even know this, I didn't and I like math, some people are young or learning and these can lead to further study, something simple is not at all, too simple because it's something to learn for curious minds that ignore it, and great minds sometimes miss the simplest details because all their thinking is based in complex thinking, so simple is there as a eventually needed reference.

[@saultube44]

***** You're a bitter attention seeker loser.

[@dantejackson8660]

You don't use your brain....

[@saultube44]

***** You're a bitter attention seeker loser.

[@saultube44]

***** You're a bitter attention seeker loser.

[@maxradke2189]

These guys actualy put high definition WW2 footage into their video! geuss what? its actualy an interview with hitler himself! if you go to 4:45 you can hear him answer the question "do you like the jews?"

[@chrisg3030]

A mysterious and beautiful recurring decimal also results from 1/1089: 0.0009182736455463728191000... with its palindromic segment consisting of successive outer to inner pairs in the 1-9 natural number sequence summing to 10. James discusses the sequence 12345679 and asks why it's missing the 8. One consequence is that this sequence sums to 37 and is also exactly divisible by 37 (another cool number which is subject of a Numberphile vid). Finally a connection between 37 and 1089: reverse and add 1089 three times to get 40293, then divide by 37 and you get 1089.

[@chrisg3030]

Nice

[@MaZzZaFaZzZa]

that is how you can zoom on fractals for hours. by not going into the center but targeting the almost closest point near the center i assume thats true :D

[@malikrath9503]

Who else seen what happened to the eight when the video started? ( I mean before it was explained )

[@Ballacha]

anyone else got a Dirk Gently vibe from this guys and the way he explains things? :D

[@LaGuerre19]

everything is connected

[@qwertyTRiG]

@@LaGuerre19 on a beach in the Bahamas.

[@chhayapatel4098]

Thank you dear friend . I like most the arithmetical specialization of different numbers .

[@JamesLaFleur]

zu der Sache ab 5:43: Das ist eine Binomische Reihe. Den Beweis gibts z.B. im Buch "Analysis 1" von Otto Forster. In meiner Ausgabe von 1992 ab Seite 182 (Satz 7) :)

[@jamesmarker3956]

Wow, I had noticed this sort of pattern just from messing around with my calculator way back in 7th grade or so. It’s cool how now, so many years later, I now finally know why it works the way it does.

[@darkmojojojo]

x/81 seems to have a lot of interesting recurring sequences: An interesting one for me is 80/81 = 0.987654320987654320...

[@ashwanishahrawat4607]

Very Nicely Explained, Thanks

[@NeptuneTart]

I'm gutted that none of my Maths classes were like this at school - showing you something INTERESTING and then explaining WHY it happens and showing you HOW to work it out for yourself is so, so satisfying compared to... "this is this formula. This is what you do with it. This will be on the test."

[@johnvonhorn2942]

+Lisa B (Clo) Schools are terrible places - day prisons for kids. I only started learning when I left and studied at the local college. Absolutely hate schools

[@PC_Simo]

@@johnvonhorn2942 Yep 😒.

[@job8]

You can be great with numbers... but I see much room for improvement in matter of paper usage :)

[@1495978707]

If I ever end up teaching math, I will start every day with something like this.

[@jwm239]

...and for the New Year 2017, hats off and round of applause for the number 129,089. Its reciprocal repeats 2,017 digits.

[@alanxoc3]

This video was really random, but awesome.