Introduction to rational and irrational numbers | Algebra I | Khan Academy

Learn what rational and irrational numbers are and how to tell them apart.
Practice this lesson yourself on KhanAcademy.org right now:
www.khanacadem...
Watch the next lesson: www.khanacadem...
Missed the previous lesson?
www.khanacadem...
Algebra I on Khan Academy: Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Algebra channel:
/ channel
Subscribe to Khan Academy: www.youtube.co...

[@rin-sd2ql]

Thx you teach better than my real math teacher

[@matthewpolanco5657]

fearirin NO REALLY

[@Supermilky0]

My current teacher is like the khan academy guy but my old teacher was trash

[@user-tp8og4ok1l]

Dumbo Cow same

[@chewyvixe9491]

My teacher is exatly like khan and hes indian

[@elchucofried5683]

My teacher is Khan

[@xedd7627]

I wish you were my teacher ;-;

[@robbi3tk]

If you're watching this video and focusing on the content, he is your teacher ;)

[@ghufranahmed3062]

My teachers at school made me learn for years but still i failed in this topic Today morning I watched this Wow i passed! Love you Khan Academy Youuuuu so great! I don't have words, I am so happy Thanks!

[@artsandcrafts6863]

Ghufran Ahmed hey are you wahaj and Ghufran cuz I think your my cousins I’m watching this in 6th grade XD

[@zethumpanza9197]

Congratulations🤩😘😜

[@AlexTheNiceGuy]

@@artsandcrafts6863 i wasnt able to find it there so i searched on yt and found the right video

[@ryannjones6456]

yes

[@walabalawalaaussie2832]

khan academy skill

[@newt122]

Iiiiiiiiiiirratinal Numbers.... Iiiiiiirtatinal Numbers..... Iiiiirrational Numbers...... X) XD I love how he says it! XD lol.

[@lizzienevels9339]

Levi Rivialle!!! On ICE lol ya

[@SreenikethanI]

haha same

[@ayesha9523]

hahahhaah................. you got him

[@madhuradharme9131]

3:50

[@nocturnalvisionmusic]

Me too still. ;)

[@user-nc6lc9ve3h]

Who is just looking down in the comments while there watching the video 😝 maybe it is just me okay 👌🏻

[@akashreddy5304]

lol im doing that rn

[@CHICKIECHIC]

💩

[@Jirehnnnn]

😂I am too

[@deadlyaak5119]

Lol

[@alizaakbar2695]

Lol me🤣🤣🤣

[@teendailymotivation9817]

Khan: " Today were gonna learn about rational numbers... rational numbersss.." Student: "Okay I get it rational num- " Khan: " Rational numberss... rationallll numbers..."

[@thiinunnu2736]

lol

[@shitpostgod2656]

Zay Zay so funny haha 😑😑😑😑😑😐😐😐😐🖕🖕🖕🖕🖕🖕🖕

[@menna7863]

Haha his name is Sal his last name is Khan

[@nasirmahmood2397]

lol your right he did say that

[@jenniferchecklover]

@@shitpostgod2656 😐

[@rubyyxlc3936]

3:41 Irrational numbers, my timestamp for future reference

[@imbaka4083]

I feel like teachers in school most of the teachers really are confusing and don't explain well youtube has helped me a LOT in math and I really thank khan academy for helping me :)

[@tableswithoutchairs1168]

i had 2 choices, watch a video my teacher sent me that explains to me the exact same thing, but takes 16 minutes, or watch this. and of coarse i chose this! this is really helpful

[@ronaldobetter4779]

Please watch the video your english teacher sent

[@tableswithoutchairs1168]

​@@ronaldobetter4779 i failed in spelling last year ok? *course

[@ronaldobetter4779]

@@tableswithoutchairs1168 oh sorry

[@ao0zero]

thanks i have a test tmrw XD

[@zerologyy5577]

whatcha get on that test bro

[@Sync-Edits]

The comment was posted 2 years ago

[@ava.42]

OriginalCornChips 😂

[@v43h]

Me to🤣

[@zh96131]

Same here altho u had the test 2 years ago but okay

[@bhoopalani7256]

I have a silly doubt.. what if 22/7 becomes something like 3.1415926535914159265359 (Just an example) Then pi has a repeating pattern of 14159265359. It should then be considered rational right? What I exactly ask is... do we have a number of digits after which we should not consider it as rational even if it repeats? I find it very hard to put into a question. But believe me, I have visited a LOT of videos on irrational numbers and only your video is satisfying. So I'm sure you understand me.

[@aarnar8518]

Ur question is confusing

[@kings-Rex]

You make perfect sense. It's a grey area that probably needs clarification

[@bhoopalani7256]

Thanks. Probably should ask gen ai I believe. Hope chatgpt doesn't bluff this time

[@ethernity9]

I love that you basically answered this within 30 seconds of starting the video. It wasn't obvious to me until you emphasized the "ratio" part of rational numbers.

[@DuckSquad4]

I'm glad the "PAUSE" button is here so people can "pause" the video whenever they like and have a look at what the person in the video is trying to teach so they can stop and have a think about it!

[@SreenikethanI]

hmm

[@aayeshafamily4022]

Hmmmm

[@user-lk9iw4qp7q]

My math teacher took 3 days to explain everything and this man takes only 5 MINUTES TO EXPLAIN.

[@rupeshranjan8769]

Which class?? Me 9th

[@glemmstengal]

There are as many as 30 different learners in a classroom and not all of them learn as fast as you or as easily as you. Get some perspective.

[@user-lk9iw4qp7q]

@@rupeshranjan8769 9th as well

[@monazcoolirani]

i think the khan academy dudes voice is close to Morgan freeman's

[@isisstrickland4525]

yes

[@crystalwolf556]

lol true

[@iviystery9704]

Not even close.

[@l.lawliet4964]

Dom Anca yeah Obama

[@callumjasmineandmax8296]

Metalma sixx Yass

[@mattpeirce2635]

😂I watched this 15 times in a row because my math regents are tomorrow

[@h._.349]

🤣

[@samalka.skakalka6786]

How are you now?

[@anvikshirsagar771]

I'm watching this before my school starts💀💀😭

[@EZ-kq9xj]

POV: you have a test tomorrow and you ARE NOT READY

[@ajtessman]

Yes... What did you get?

[@EZ-kq9xj]

@@ajtessman a 67 😭

[@ajtessman]

@@EZ-kq9xj I got a 45 😭😭 then I did a retake and got 70

[@mrxarch]

our teacher was teaching us for a month just for this and no 1 learned it but now i fully understanded it in 5 minutes i wish i could pay some thing for u

[@miasims7575]

I still can’t really understand it, but I just needed to know how do you get a irrational number.. so thanks 🙃

[@shubhangi__8112]

here too

[@humanyter7214]

@miasims7575 still don't get it?

[@themecha1698]

Thanks khan academy... today at school we were learning Zeno's paradox and I could not understand it. Now after watching this amazing video, I am happy to say that now I understand it

[@that_one_septiplier_fan1881]

This seems like highschool.... Only a 7th grader... ;-;

[@Dream-ql9hg]

Im a 6th grader ;~;

[@dumeka-miller8191]

Me too

[@mahiranasiraziz]

Manly Fairies me too😘😘

[@amyshin1693]

i wonder "why" its called "introduction" to rational and irrational numbers...

[@4MY4KIDS]

That_One_Septiplier_Fan Ima 6th grader... this is too hard for me!

[@suhebkhan8139]

FANTASTIC WAY OF TEACHING SIR... AWESOME

[@MaxxAndKfox]

is your caps lock stuck on?

[@foxyolk]

​@@MaxxAndKfoxfr

[@druhanperera]

The one time I pay attention in class

[@lynxth3wuf969]

thank you so much! this helped a ton. your voice is so soothing to listen to and you're simple and straight to the point. I like it! 🌻

[@MohdZaheeruddins]

I am 35 and learning this.. wish I had access to internet during school days

[@arifafahmida4045]

Very bad.but why r u learning this useless thing?learn coding or languages or anything u like

[@MohdZaheeruddins]

@@arifafahmida4045 learning coding or csc without basics in math...

[@HUZIAFA.KHAN123]

​@@MohdZaheeruddinsbro your lucky you didnt had Internet its distraction bro at your time you had 4 distractions now we have 40 there's difference bro

[@Pix_or_not]

10yrs later and ur still teaching me new things. Thank you for being in my life as an ACCUAL teacher

[@hannahhughes3866]

bruh i still can’t get it 😭

[@royaleplayzyt9690]

Is it just me or is Sal's voice soooo calm!

[@ashleyp8328]

Is anyone else 23, graduated from college, and only here reviewing because DAT Bootcamp told you to? .... Just me? Okay

[@SreenikethanI]

haha (8th grader here)

[@whatthestopmotion9242]

@@SreenikethanI same

[@brendenhonaker605]

same lol

[@nanoh9107]

6th

[@_daesung7723]

Mad Scientress no aha i’m in 8th

[@HungerSlice]

Amazing explanation. I feel a little obfuscated how the majority of your viewers did not understand. There could not be a better explanation. Some ignorant people are asking peculiar and sarcastic questions like : What's a rational number? Didn't you freaking the video? Its a number that is either recurring or can be placed in a ratio/fraction format! Thank you so much for this video. I've been a little bewildered by this topic. I'm currently in grade of and definitely know that there are millions of topics to cover and a long journey stands before me!

[@HungerSlice]

Didn't you freaking watch** the video? I can't seem to find the edit button

[@HungerSlice]

Grade 9* It's*

[@AdamKrivoshein]

Thanks so much. Your videos are exceedingly helpful in a simple easy way.

[@rakeshthakur8384]

You are god gifted men. Because no teacher can explain this chapter in 5min.

[@LearnFirstEarnNext]

The Ratio between the Circumference and Diameter of any Circular objects like Small Ring to Big Moon always is π (Pi)... For example, Take a small Ring. Using thread measure it's Circumference (C) and Diameter (d). Now, C/d = one answer in Numbers.... Next imagine you are measuring Moon Circumference (C) and it's Diameter length. The ratio is: C/d = gives the same answer in number what we got in the case of small Ring. Conclusion:. C/d = Same number every time... That same number is π.... C/d = π . So the circumference of a Circle formula is C/d = π C = πd C = π (2r) C = 2πr units... Pi is the 16 th Letter of Greek Alphabet.... Almost maximum Maths Symbols we are using is Greek Language Letters.... Difference Between Rational and Irrational Numbers: Rational Number: It has Non-Terminating and Repeating (Recurring) places of Decimals. Example: 10/3 = 3.33333333... 22/7 = 3.142857 142857 142857..... Irrational Number: It has Non-Terminating and Non-Recurring places of Decimals. Example: √2 = 1.412135623 π = 3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ... Hence Real Numbers = The Set t of Rational Numbers + The Set of Irrational Numbers...

[@gargeeprakash]

Every students bias is KHAN ACEDEMY!! Thanks a ton.

[@akssagir5411]

I wish i had these time of foreign teacher in pakistan.

[@chur1k5]

Khan Academy is fantastic, although it needs some upgrades on their website, Other things AMAZING! I have a good math teacher (Indian obviously) But he talks fast :/ So I searched this on KZbin for my exam, I am confident with this, Thanks.

[@mcmuffin446]

if anyone is still confused,here is the definition in simple terms *Rational Numbers* : All the numbers in the form of p/q,aka fraction,where "q", aka denominator,is not a zero are called "rational number".It's denoted with the capital letter "Q" *Example* : {2/6,4/8,9/4,....} *Irrational number* :literally any number with the square root sign "√'" *example* : {√'3,√'8,√'100,√'pi.....}

[@fearnot90sm]

Except for perfect squares. square root of 100 is equal to 10 which is a rational number

[@sirsparks7517]

helpful info thanks

[@brook.f]

"And we call these numbers, Irrational, iiraationalll, irraaaatttiiiooonallll, iRaTiOnALlLLLLlllLLLLlLLLlL LlllllllL" 👏👏😂

[@abdelrahmanalaa1219]

Brooklynn Fynn put it on ×0.25

[@mr.trollge766]

I like these types of videos, not because of the math, but because they way he writes perfectly with that writer

[@gabelanning3600]

POV. End of year test are coming up and you haven’t learned anything😂

[@Count_Courage]

Im here because im refreshing my memory for college working from Pre Algebra to Calculus my father is a math teacher and gave me his books

[@Jess-cw1is]

thanks I finally found a video that helps me:) hopefully I pass my test tomorrow:)thanks

[@thoughboy866]

Did you pass?

[@aquazna247]

you pass?

[@cailindubh]

Don’t leave us hanging Jess

[@arynx1245]

i love how he sounds excited even talking about math, it helped me understand this more somehow :)

[@Incepter.]

WOW MATH RATIONAL AND IRRATIONAL NUMBERS IS SO EASY I NEEDED THIS FOR MY SCHOOL CLASS THANKS KHAN ACADREMDY

[@gamingprisoner593]

Academy

[@praisejah4120]

Thank you Khan for the hashtag, I was put into remedial classes recently and i started to believe Natural Selection, I felt my existence was simply to be inferior by nature . Telling me that gives me just confidence and motivation to work harder and catch up , I would like to make a difference in the world 🌎 one day . I’ll play an important role in making the quality of life better for all life , I won’t stop 🛑 😤

[@Oriss81]

When there’s a break during lecture I come here to actually understand it.

[@ayatbrown1913]

Bro u teach me better than my math Teacher

[@bernardmcintyre1550]

a very educational video I recommend it for teachers all over the world

[@user-ok2be9qt7x]

How could this video be so beautiful? How could this teacher be so amazing?!!! I can't believe this video was 9 years ago..

[@MukeshKumar-qz8xt]

Thank you very much sir for clear my concept on rational and irrational number

[@vinered4096]

You are so awesome, let the haters hate because they're nothing in life.

[@SreenikethanI]

True...

[@SreenikethanI]

*EnglishPremierLeague Central* kind-of yes Btw I am in 8th grade now

[@kirakingdomz]

I understood nothing, but thanks.

[@christipotgieter9302]

Guys!! Sal said "irrational numbers" like four times in a row(4:00). Great video, BTW

[@smithavijay332003]

Awesome it became so easy for me and helped mea a lot thanks a lot

[@umarshahidsahito9425]

Your way us very precise. And you define the main thing that you've mentioned in the topic. You are teaching very nicely but i would request you to define other terms also. Just like if you are teaching rational number and you've mentioned the recurring decimals now let us know what is recurring decimal and how can it be found?

[@gabys.cherry8148]

I really hate math and honestly I would rather have all my nails pulled out one by one than ever do math again but I have to do it and if I do it I might as well do it correctly

[@SreenikethanI]

oh God chill

[@chickennugget9742]

Why the nails though. Like...OW, how are you gonna scratch yourself?

[@farah886]

ouchhh

[@farah886]

Ayedan Moscal ouch at the thought of your nails being pulled out

[@RaspberryV3]

I would rather put a nail under my toenail, and smash that nail against a wall repeatedly, then stab a knife into my arm then do math again.

[@Scholarszilla]

By taking inspiration from your videos , Making videos in Hindi / Urdu. You are great.

[@moizkhalid2714]

good to revise basic concept 👉💯✔👍✌

[@user-tp8og4ok1l]

7th grade here we will have our exam on monday good luck to me

[@aeriumduerre7272]

Same, co-carat.

[@imadejaber126]

its a good thing his explanation is very simple you make you understand queckly

[@familypack4114]

YOU CAN'T SPELL YOU NOOB

[@_daesung7723]

family pack *You can’t spell, you noob.

[@yeeyeegaming2465]

_강대성Daesung r/roastme

[@yuzunoii8523]

few hours left until exam and im so glad i found this helpful vid :0 and also...gahdamn that voice tho. its majestic ^3^

[@maymamii]

Super great video it helped me a lot! thanks bro. :)

[@jaugerot6401]

This is a review I have to use for midterms tomorrow

[@jessicaspencer4908]

what app do you use for your videos and how much did it cost???

[@jakedavis7950]

That's photoshop. I think its a modifier/add on or something that makes it to where you can draw on it like a chalk board.

[@superduckmansuperduckman9504]

Yes thank you my online school is so dumb and does not teach me in a way I can understand this taught me more than the computer did which just expected me to understand

[@MooMooMath]

Thanks for the clear explanation of rational and irrational numbers. Putting a label on different numbers can be confusing. I liked your video so muchI linked to your video in my video notes.

[@rasbanikaur2122]

Rational numbers are ratios of integers, including decimals with patterns. Irrational numbers, like pi and the square root of2, never terminate or repeat. There is always an irrational number between any two rational numbers, and the sum or product of an irrational and rational number is also irrational. [00:00] Rational numbers are ratios of integers, including non-integers like 3.75, which can be represented as 375/100 or 15/4. - Integers are rational numbers - Non-integer rational numbers can be represented as the ratio of two integers - Examples of non-integer rational numbers include 3.75, which can be represented as 375/100, 750/200, or 15/4 [01:56] Rational numbers can be represented as the ratio of two integers, but some famous numbers in mathematics are not rational. - Rational numbers can be expressed as a fraction of two integers - Repeating decimals can also be represented as the ratio of two integers - Some famous numbers in mathematics, such as pi, are not rational [03:47] Irrational numbers are exotic but not uncommon, with an infinite number between any two rational numbers. - There is always at least one irrational number between any two rational numbers - Taking the square root of any non-perfect square or adding an irrational and a rational number results in an irrational number

[@selenator5108]

I still don't understand🤦🏽‍♀️

[@arifafahmida4045]

See more videos

[@cadywhite2337]

So helpful!! Even my own teachers say if I don’t understand it to look it up on khan academy 😂

[@sheikhirshadsheikh]

Easy way of learning

[@getit900]

Irshad Sheikh ģ

[@vanshchojar4642]

I guess you should my math teacher

[@vickysuleman1135]

so what is a rational number...

[@gamithadithya4166]

lol

[@ebenezergetachew5318]

it is a number that you can put as fraction. RATIO

[@vinodkumarrohilla3808]

Vicky suleman

[@SreenikethanI]

0:01 here you go

[@l.lawliet4964]

Vicky suleman Puri Mahabharat ho gye or puch rhe ho ram kon hai 😂😂

[@angxls7322]

Thank god we found you we didn't understand this so me and my mom learned something before I failed

[@robertcastaneda7562]

My school teacher really did send me here during Corona

[@miriamrodriguez6742]

Actually same

[@JEsGamingLife]

When I was younger, I thought e was rational (2.71828 and 1828 just keeps on repeating forever.) I didn't know the concept of e back then.

[@ethangriffeth3679]

IM IN FIFTH GRADE Y'ALL

[@xt5472]

I'm in 6th grade yall

[@EinsteinIbraheem]

@@xt5472 im in grade 8 yall

[@PrincessYonna1]

🤣12th

[@astram957]

my math teacher just puts these kinds of videos and goes away

[@joselynrodezno657]

This was mad helpful!

[@iminlovewithyoongioof.]

fire profile pic bro

[@Stellajack04]

Very simply explained. Thank you.

[@chillz6793]

Lol he kept repeating each title like a thousand times! Thx really helped

[@muhamaddak3203]

You still alive?

[@samalka.skakalka6786]

Hi I’m from Kazakhstan ( English is my 3rd language. I’m not native speaker ) and I understand this topic!

[@sandipansen2760]

Thanks.This helped!

[@kyleweichert1553]

Such an ASMR voice

[@bangtanarmy4546]

Really Appreciate your work . 💯💯

[@victoriaeghe8754]

I love math because if you get the real picture of it, it becomes very easy.All you need to do is to spend time in it and don't underate yourself

[@gursimratgill7872]

Ye

[@alhjooj2002]

thank you sooo much :)

[@didadiy2548]

thank you I like all you're videos

[@raghadkhalaf2545]

i cant understand any thing 😐😐😐😐

[@ebenezergetachew5318]

Go to Math is Fun website they will explain it better.

[@lourdeslee2762]

Me too he talk fast

[@ayesha9523]

honesty.....is a good thing good

[@devithedevilwip348]

Raghad Khalaf same XD

[@jkd0114]

sAme

[@whimsicalgolde]

I just want to say this is a good refresher. Also, this is good to use to learn on your own more. I am using this as a refresher, due to being a few years and I have a test to take. But if you are just on your own and you can get to KZbin. This is very good.

[@gamithadithya4166]

thank you

[@Hashimrabia]

Way better than school id rather take these lessons

[@azkasaqib408]

7 years later this video has helped me pass my online exams during quarantine

[@jonykhan4395]

Good work! you said division of any two Integer is the result of a rational number. The division of two irrational numbers can also be a rational number. For example: √2 /√2 =1 which is rational number. So why everyone on KZbin say p/q both MUST BE the numbers from the Integer set??

[@HouseofWeh]

I appreciate your teaching style! Thank you!!!

[@yuvaraja882]

Thank you so much for your clear explanation!

[@ASMRkiddos]

Thank you. :)

[@peepawwillynyopagodna7733]

Omg thank you so much! And when i first heard your voice i literally thought of ranboo!! You sound like him and i think this is how ranboo would teach 🤣

[@ayanakif7962]

Comment section not dead even after 7 years

[@breadedbread9022]

People want a "Rational" explanation... I'm so sorry

[@rozegon6920]

your clear voice and the way you teach are so Precise , direct and GREAT like you know what , i liked it .. thank you :)

[@SreenikethanI]

I know right! So true