Converting repeating decimals to fractions 2 | Linear equations | Algebra I | Khan Academy

[@kevbeckonz]

I love how this guy explains things.. I have advanced 7th grade math and it's tough sometimes but I always watch these videos and it makes complete sense now. Thanks!!

[@EpicRobloxTomboy]

in 6th grade.

[@akhilkatragadda1478]

so stupid

[@akhilkatragadda1478]

you too you cannot take algebra in the 6th grade

[@moniiiiiiiiii]

Akhil Katragadda depends lmfao

[@irvingrivera4302]

I have advanced 7th grd math too

[@djancak]

WHY AM I JUST NOW LEARNING THIS?

[@isha9300]

hello, person from 8 years ago. I came to tell you that you earned approximately 1 like per year.

[@isha9300]

@@djancak ok but that's still so unexpected. You responded within hours. 8 years is a lot you know.

[@isha9300]

@Chaitanya Joshi oh wow, I’m famous. Thanks for the reminder.

[@vdex2866]

@Chaitanya Joshi hello person from 1 month ago, i want to tell to you that you got 2 likes in a month.

[@NXL1204]

Hello

[@ocdfreak]

I love that I'm in Partial Differential equations and I've never learned this. It seems so simple and elegant!

[@Boyld_eggg]

I LOVE YOU KHAN ACADEMY! YOU MAKE MATH MORE EASY!💖💯

[@tyrant8541]

You are a good maths teacher :3

[@SikariGamer-ws4op]

Thanks teacher 🤗🤗 it he help me very much.

[@AnHonestApe]

you need captioning on these videos. And it's funny because when i try to see something on the screen that you wrote, I scroll up on my screen. lol.

[@martialartsism]

omg this video helped me sooooooooooooooooooooooooooooooooooooooo much!!!

[@mojeedabimbola3019]

omg I love this videooooo

[@mohammadatiq6142]

Omg same sis

[@valeriasavostenko2220]

Think video really helped me to study for an upcoming math test!!!👍

[@blinksandthepinks79]

5:07 i mean you could have just multipled 0.714.... by 1000 and 10, then subtract 7.14 from 714.14 which equals 707/990 ....a lot easier !

[@tristenscott5754]

does that mean that you have to multiply by 10 always?

[@ericka781]

yes @@tristenscott5754

[@MathAngels-js9tm]

Thank you so so so much. you make even the hardest seeming math concepts so straightforward. much appreciated!

[@Gokul2007-ih1dv]

i have seen all 92 videos of algebra playlist

[@kwesigaalex4765]

Well presented. Wanted to memorise a ratio with recurring decimals but in fractions for future accurate use and couldn't recall this method.

[@drflopper1445]

Thank you so much! Everyone should most certainly subscribe to you.

[@griftorifto2]

Theres another simpler way of doing this. Although i couldnt explain through yt comments

[@Sz_Cl1ps]

just reminding you of this comment from twelve years ago ;)

[@PrinceHill]

what program are you using to draw the stuff

[@oatmilkpeek1291]

SmoothDraw3 i believe

[@MrHuangfeihong]

This is Khan power (im serious)

[@monali453]

Explained extremely well and made is so easy to understand for my 11 yr old son… thank you

[@alexi0186]

Monali Dikshit lolllllll

[@GamingPaxels]

Without Khan Academy, I wouldn't be ahead by 2 grades in school.

[@shamikh5301]

You are a great teacher. Not only a mathematics teacher but you are brilliant at teaching everything. I can understand really well after listening to your explanations and doing exercises on your website.

[@VictoriaLiLittlePianist]

❤❤❤😊love it

[@Wisdom7527]

Thanks Sal for this great playlist, it's really a treasure.

[@johnbob1266]

Thanks once again Sal Khan!

[@prciusgrnmo5614]

what if there's a zero after the decimal point?

[@naniidoodles]

If we're dealing with 0. 036... Then we multiply it by 10 to get 0.36... And that would be our 10x We then want a whole number of the recurring decimal so we earn that by multiplying 0.036.... by a 1000 to get 36.36... And that would be our 1000x Now we know what 10x is and what our 1000x is and now we subtract 10x from 1000x 10x - 1000x = 36.3636... - 0.3636... 990x = 36 We then divide both sides by 990 to get x x = 2/55 which is also = 0.0363636.... (I know your comment is old, shhh)

[@hellowillow-5951]

I have pre-algebra so this helped a whole lot!

[@ForeverWiked]

In case anyone cares, you can use this to prove .999 repeating is equal to 1

[@Shivid.2020]

THIS IS SO GENIUS

[@NooNooBaby11]

Yes good job

[@jeremymiller4189]

Converting various repeating decimals to fractions and doing basic arithematic is probably the best way to go if you want to teach this as soon as possible.

[@ThisuraYapa]

Great video! Thanks for making me understand !!

[@eyyuptuncersabanl3908]

Teşekkürler

[@angelc1562]

THANK YOU I NEEDED HELP ON THE SECOND PROBLEM THANKS U

[@lucasquek710]

this video is great! It has helped me to understand a lot!

[@jocelynchai9602]

hi lucas

[@lucasquek710]

Oops wrong one

[@lucasquek710]

Autocorrect sucks

[@openmoose]

@Vaylemn No, that can't be done. Irrationals cannot be converted into fractions. Another name for a fraction is "ratio", that's why any number that cannot be written with a ratio is called "irrational".

[@zayzay14672]

Thankyouuuuuuuu

[@noam.1563]

What are you using to represent this?

[@toughingen]

Nice video. But why didn't you immediately multiply by 1000 in the second example? In the end you still have to multiply by another 10 to get rid of the decimal.

[@maximcostiuc9740]

NOOOOO SOMEONE DISLIKED IT PLEASE DONT PUT IT BACK AT 69

[@nm800]

very late comment, but the last one 3(257/999) is not to be meant as a multiplication right? Because when you do it it doesn't give back 3.257

[@Rani-th1hu]

Thank you!!

[@TehMikstPinoy]

Seriously, it's THIS easy? T___T; I hate my math prof :(

[@SuperGraciemom]

Hello person from 9 years ago, looks like im not the only one struggling on this

[@jaeschel69]

THANK YOU YOUR AMAZING!!!

[@ItsMeJosh01]

0:44 "Linin' 'em up!!" :)

[@daisyr6415]

Thank you so much!!!!

[@khice6922]

Subbed

[@knowledgeuni497]

3:21 moment le plus important qui explique comment calculer les problèmes difficiles

[@min_baniedits5972]

3:36 0.714 Sir, Can we multiply this by 10 so that it becomes 7.14141414...... in this case The repeating numbers stays same and subtraction can be done too.

[@brauliosolanoreyes2038]

Ya hice todo ahora cuan sigue me pasan toda la lista de reproducción de cada álgebra que curso sigue? Pre álgebra o álgebra 2 o no se 😔

[@andrestoledo5329]

My mom is making me watch these because it got a 96 in math

[@nmaliyt2062]

No words

[@aammarkhan2661]

Taking algebra 1 in 7th grade. This helped a lot.

[@jigyasamadan]

Thxxxxxxxxxxxxxd

[@sarahullah6604]

3:03

[@Quintynnandjvplay]

where did you get minus x from?

[@Angious]

drawing program?

[@openmoose]

@oSoloDolo If 0.999... != 1, then there is at least one number between them. Further, because the Real Numbers are dense, there should be infinitely many numbers between them. Can you find even one? Alternately, proving that there are no such numbers is sufficient to prove that the two are equal. Calculus isn't the only way, or even the best way, of proving things.

[@GetMeThere1]

Before this demonstration I had never realized that one can write ANY REPEAT, of any length that suits one's fancy, and there is a straightforward "fraction" that represents it. It's obvious, yet I never thought of it that way--I somehow thought that repeating decimals were "special."

[@fabianrobinson1800]

thanks times a million

[@aydenhale8032]

very useful

[@tomnguyen4048]

There's a much easier way of doing the last problem.... just say x=0.257257..., instead of 3.257... and use the method from problem 1 to find that x=257/999. Thurrforrrre: 3.257... = 3 + x = 3 and 257/999. Wouldn't have to long-divide by 999.

[@moniiiiiiiiii]

Tom Nguyen helpful for students without access to calculators, (we just have to show our solutions when using calcs)

[@tomnguyen4048]

The Noobness The whole point is to be able to do this without calculators, right?

[@HikikomoriDev]

MAGIC.

[@shrleenkumar6632]

j

[@aminaashour8675]

Would about converting it into improper fractions???

[@_imnic_879]

+Amina Ashour like 37 over 8? just convert normally to mixed fractions? Is what i would do, im sure you would only do if it was asked to be answered as a proper fraction

[@muhammadghibby2499]

what anime do you watch

[@Memyself900]

Learning maths. again :))))

[@angadtendulkar292]

Or... You could just say: There are 2 repeating digits so now get the 2 repeating digits over two 9's. It is simpler.

[@maximcostiuc9740]

please dont dislike the video anymore its at exactly 69 likes

[@TFGuy]

I'll never be as smart as you.

[@royalspike2]

isn't there some other way to do this. i did it in my calculus class. but it sure was not as easy as this.

[@oSoloDolo]

@oSoloDolo that should say 0.999... = 1

[@oSoloDolo]

@royalspike2 It wasn't easy as this because this is mathematically incorrect, although it will give you a correct answer. You probably learned the correct way.

[@jeremymiller4189]

That's like saying 1.888... - 0.888.... doesn't equal 1 even though 0.888... is nowhere near infinity.

[@52blue42]

It would be easier to subtract the nonrepeating numbers then add them back on later. Because the denominator of the fractions of repeating numbers is always 10^x - 1 (then divide or multiply by 10^x) Example: 0.7 *14141414* .... = ( *14* /99)/10 + 0.7 3. *257257* ... = *257* /999 + 3 20. *123451234512345* .... = *12345* /99999 + 20 60 *4.04404404* ... = ( *404* /999) * 10 + 600 Then, just convert the improper fractions to proper fractions

[@derf124]

eah

[@tonyboro3981]

Would this appear on the calculator paper or non calculator paper

[@poppyella2205]

In my english exams this is likely to appear on both, so for you too, wherever you're from, its highly likely to be on both or either, however on non calc the divisions may be slightly less harsh

[@poppyella2205]

disclaimer: by english exams i meant my maths exams in England! ((:

[@bazdaboos6726]

no calculator in the uk

[@Tayohni]

In what grade is this taught?

[@tristenscott5754]

7-8th its pre algebra

[@Najar_M]

Dude i just needed help with one like this 7.08

[@codenamelux8683]

Okay okay hold on

[@adria999]

im in 8th and i still cant do math sorry guys

[@jamiejohnson7399]

Math sucks thanks for helping

[@shazminkamali7495]

Recurring.....

[@oSoloDolo]

@ForeverWiked It's a pretty weak proof, though. The technique he's using isn't quite mathematically valid because infinity minus infinity doesn't equal zero, so an infinite number of digits after a decimal point minus an infinite number of the same digits behind a decimal point will not leave you with a whole number. In relation to your proof, 9.999... - 0.999... != 9. If you wanna prove that 0.999... - 1 like a boss, use some calculus. :)

[@midgeamoo]

@khanacademy Sal, could you do something about the proof using this method of 1 = 0.999999....? I wouldn't mind seeing the myth approved/debunked by somebody that knows what they're talking about :p

[@legsaysstuff1877]

im confused

[@oSoloDolo]

@midgeamoo It's not a myth; it's fact. If you really want to prove it, you need calculus.

[@bythemile18]

@Bumperpegasus It's not Sal's fault...

[@anoneemous406]

What if only one number is repeating? like 0.60, and only the zero is repeating?

[@christinefair2637]

Tornado- Tutorials and More! I dont think a 0 can repeat. Once there is a zero at the end it stops

[@anoneemous406]

Ok thanks!

[@craftbuilder2142]

Tornado- Tutorials and More! All none repeating numbers have a repeating zero. So 6 is equal to 6.00000000000000 and so on.

[@anoneemous406]

ok thanks

[@amanc9835]

Tornado- Tutorials and More! It depends where the line is over

[@mmmoro1819]

dove è l'italiano?????

[@oSoloDolo]

@glitch232 0.999.... DOES equal one. Calculus is the best way I know to prove this, 0.999... being an infinite sum and all that. :/

[@loveoverwatch1553]

This guy makes 0 sense.

[@funwithfamfun]

How?!?!?!

[@SuttonAlternative]

why do i have to learn this crap???

[@jadonjung5074]

the numerator is not repeating part and the denominator is how many nine's and how many zero's. That is what my mom told me

[@Bumperpegasus]

@djancak I know. Sal's a botch for tricking us

[@JonathanBartlesSWBGaming]

3254/999 can't be converted to a proper fraction.

[@matthew9135]

He sounds like a broken record. 7...14 14 1414 14 14.

[@Glados1080]

This didn't help at all

[@jetpaq]

+irlvidsLoL irlvidsFtW keep watching until it does..and practice. If you still don't get it,you may be in a place too advanced for your level of math. go back and learn fractions on khan academy, from the basics. He will never steer you wrong..the guys a genius.. and so are you, u just need to practice a little :)

[@Glados1080]

+jetpaq Haha I'm not 7.

[@jetpaq]

irlvidsLoL irlvidsFtW well its ok iof you dont get it, but going back to basics doesnt mean your underage or incompetent. Its just that mastery of each level leading up to this one will make your understanding more effectual. Its the premise the entire khanacademy is built on. There is a "hole" in your understanding of fractions, so in order to patch it up, u need to start from the bottom of THAT hill and climb up , at your oewn pace..i mean..it could take a couple days..or hours..but dont cop out and say you dont understand it and think no one here wont try to help..because we will.

[@jetpaq]

***** right on !, and thanks

[@aiymgulabdykarimova]

thank u so much!

[@juliachen-cn6144]

5:35