This also works with numbers that repeat like 4.56785678…. Just take the amount of numbers repeating, multiply by a 1 followed by that many zeroes (in that case 4 so 10000) and do the same thing.
Bro I’m not gonna show you if you really want do it yourself. The math makes sense, but if you still don’t understand, take x= 6.252525… multiply both sides by 100, subtract x and get 99x=619, so the fraction is 619/99 (I think)
I liked this. The thing is... with problems there are multiple ways of solving... but everyone thinks their way is the best. But I like your lectures. Thank you.
This is fascinating....as a person who always just kinda "understood" what was going on with the maths without being taught, seeing the actual explicitly defined version of what I've always just kinda done in my head is interesting.
Actually this can be extended further. It goes like this: 1. Take the block of numbers that is repeating. 2. Divide it by total number of digits in that repeating block. 3. Example: .357835783578 is 3578/9999.
@@ChristoferKelly what he meant is that there are 4 repeating digits, so you divide it by 4 9's. For example, if I had something like 0.1234512345, i would divide it by 5 "9's" so that the fraction would be 12345/99999 (yes i know you can simplify that)
@@AnthonyDoesTH-cam He meant to say that whatever the block is that repeats, to find the fractional form of the given number, create a fraction where the numerator is the block and the denominator is a string of 9s that has the same length as the block. For example, 0.568455684556845... is equal to 56845/99999, because the block is 56845 and the block has 5 characters in it.
Wait - so all repeating decimals can be written as the sequence of numbers that get repeated over as many 9s as there are numbers in the sequence, e.g. 0.123123... = 123/999. That's slick!
@@Daniel31216 but you can though? i dont deny there being other proffs, but this one can be used. i was only pointing out a potential party trick that this method can produce
I love the fact that I can just do this on the calculator, meaning that I don't HAVE to be able to do this, but I GET to do it and have fun with it. Thank you for all the cool methods sir, it really makes maths fun.
A faster trick is to take the repeating part and put it over the same number of 9s. For example 0.123123123 = 123/999. But I didn't know how to prove this trick so thanks for the video!
I majored in math and physics. Usually the weakest math majors ended up teaching at the high school level. In order to work in the math lab you had to pass a test of 5 or six word problems. It was sad that a large percentage if senior teaching majors couldn't even work rudimentary problems. To make matters worse, at math departments across the country, the weakest teachers end up teaching the students that are the farthest behind.
Also worth noting that you don't have to multiply by 10 each time, the thing is, you have to get one part of the number out of the decimel, so for example if u were to convert 0.265265265... you should multiply by 1000 and continue the calculation....
I love the fact that when to try to get a fraction for 0.99999....... it becomes x = 0.99.. 10x = 9.9999.... So 9x = 9.9999 - 0.999 = 9 So 9x = 9 So x = 9/9 = 1 So basically it gives 0.9999999 = 1
To find the digit sum of any number faster, strike out all 9s, and the remaining number would be the digit sum. E.g. 1) say for 456, strike out 4 and 5, because their total is 9. The remainder is 6, so 6 is the digit sum. 2) say for 879, strike out 9, remaining is 87, take out 1 from 7, add to 8 to get 9, which can be strike off, final number remaining is 6 (7 - 1). This striking out all 9s technique can be used for any number to find the digit sums. Thanks to Vedic Maths!
Отличный преподаватель. Я совсем не понимаю что он говорит, но понял как он нашел ответ. Это на сколько просто, что мне стыдно, что я сам до этого не дошел
They always taught me to write 0,5 with the periodic line on the 5, then to rewrite all without the stating zero and the periodic fives, subtract all that isnt part of the period (in this case it can be avoided), then it becomes 5, just add an 9 at denominator (one for every periodic digit, so only 1 because it is only the 5 here)
Genius is the natural ability to see things that others don't. If one doesn't have that natural ability then one has to focus and work better to become a "genius".
very good and easy to remember and understand. very simple to remember the idea to multiply. so you align the digits of the repeting part and you can eliminate it by subtraction. in the school they taught me a very hard to remember fraction rule
This is the same method used in the simplest proof of 0.99999... = 1. Just like he showed that 0.55555... = 5/9, you use the same procedure to show that 0.99999... = 9/9, which is just 1.
It also helps knowing that the only way to get a number to repeat is by dividing by 9. This is also the reason why 0.99 (repeating) is equal to 1. To get 0.99 (repeating), you would have to divide 9/9, and that's just 1.
Thank you for your videos. They remind me of math classes I took in high school. Truth here. A few of us hs-students would go to school an hour early and work math problems--this was at 7am. Our math instructor always wore a suit and tie. Most of this would seem a little odd these days. Believe it or not we thought math was fun - no calculators allowed 😆 To this day when dealing with simple transactions I can beat the computer response when shopping. People give me a puzzled look when I tell them the answer. My policy is stay humble and be an old nerd. Also I was the only girl there. 😮😊
In school I had learned only the result of this process. That is, whenever you have zero-point-repeating-numbers, the answer is one of those repeating sequences divided by as many nines as there are digits. That is, 0.111111... is 1/9; 0.121212... is 12/99; 0.123123 is 123/999, and so on. But we never went over the reason _why_ this works. And that's worth learning, because studying math isn't meant to be just learning a series of rules. It's about understanding numbers and how to play with them. We learn existing solutions to existing problems so that we can develop new solutions to new problems. This is especially true today, when we're all carrying a very sophisticated calculator and mathematical analyzer in our pockets. There's not really any merit in learning a bunch of processes if the machine in our pockets is going to get the answer more quickly and with fewer errors. Basically, we have to ask ourselves, what is the point of still learning math these days? And if learning math is just about studying the programmatic processes that our meat-brains do so slowly, the answer would kind of have to be "Eгг".
This is an example of a single digit repeating. So this method can be used exactly nine times. Use the same principle to × 100 for 2 digits, 1000 for 3, etc.
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If all student get a great instructor like this, no one will ever hate math
Not really.
You are right
The problem are the students
@@shalk8769 yes, thats true
I wouldn't like my teacher to write in that handwriting and those chalk noises are annoying, I have to mute my audio for peace
He got really excited writing that 9 in the x = 5/9 near the end, haha
Yes, you can tell from the ugly tail of 9
you are also excited to see that😊
@@MrKhan10000 ahahahahhaha LMAO
You want an instructor with life in them, keeps you focused and wanting to learn more haha
@@david_r lmaooooo
The sound of the chalk clicking on the board is just enough to make me learn algebra
It’s so satisfying
Really... it keeps our attention to what he is saying, perrrfecttt
Crisp, quick, accurate equals efficiency
Everything seems so easy when it was lead in the right direction...
*led
*is
Bro, in India we used to do these in class 4. Olympiad book
@@darkaryan4535 Yet in India people take dumps in the street.
@@toaster4693 You're gonna find people like that in any country what's yoir point?
That was elegant. These simple, yet efficient, videos give me the confidence to keep trying to relearn math
Do it!
I really like the idea of using repeating decimals as a way of introducing series, like 0.99999.. = 1.
Oh cool! I didn't even catch that this is also a proof for that equivalence!
🤓
This also works with numbers that repeat like 4.56785678…. Just take the amount of numbers repeating, multiply by a 1 followed by that many zeroes (in that case 4 so 10000) and do the same thing.
Show me.
Bro I’m not gonna show you if you really want do it yourself. The math makes sense, but if you still don’t understand, take x= 6.252525… multiply both sides by 100, subtract x and get 99x=619, so the fraction is 619/99 (I think)
@@thereal_pixel_phantom
Alr ty
Not 4.567845678?
@ no, the four doesnt repeat only the decimal im pretty sure
Am I the only one that got a light bulb 15 years later !!! Amazing! Thank you
I liked this. The thing is... with problems there are multiple ways of solving... but everyone thinks their way is the best. But I like your lectures. Thank you.
This is fascinating....as a person who always just kinda "understood" what was going on with the maths without being taught, seeing the actual explicitly defined version of what I've always just kinda done in my head is interesting.
Try to be come an analyst for a firm or solo ... we need people like you doing useful things...
I always knew this with repeating single-digits and 9, but never knew the proof for it. Thank you!
I learned the formula for convertion like 10 years ago now and only now realised how it actually make sense lol
I wished I had a teacher like him back when I was in school.
Actually this can be extended further. It goes like this:
1. Take the block of numbers that is repeating.
2. Divide it by total number of digits in that repeating block.
3. Example: .357835783578 is 3578/9999.
thanks, THIS is the proper (easiest, direct) way to solve that question
Except there arent 9999 digits in the repeating block.
@@ChristoferKelly what he meant is that there are 4 repeating digits, so you divide it by 4 9's.
For example, if I had something like 0.1234512345, i would divide it by 5 "9's" so that the fraction would be 12345/99999 (yes i know you can simplify that)
This just confused me way more, please stop
@@AnthonyDoesTH-cam He meant to say that whatever the block is that repeats, to find the fractional form of the given number, create a fraction where the numerator is the block and the denominator is a string of 9s that has the same length as the block.
For example, 0.568455684556845... is equal to 56845/99999, because the block is 56845 and the block has 5 characters in it.
Wait - so all repeating decimals can be written as the sequence of numbers that get repeated over as many 9s as there are numbers in the sequence, e.g. 0.123123... = 123/999. That's slick!
I made exactly this calc... wow before I read the comments
By definition of an irrational number being nonrepeating, you can infer that a repeating number can be represented as a ratio of integers p/q.
it also means that you can proof 9/9 to be both 1 and 0.999...
@@vanillabigm6810 You don’t prove 0.99… = 1 using this method.
@@Daniel31216 but you can though? i dont deny there being other proffs, but this one can be used. i was only pointing out a potential party trick that this method can produce
Once again, the never-ending wonder and beauty of mathematics! Thank you, Mr. H.
Wow, thank you!
What a good teacher, he took less than a minute to explain our lesson on math, but my teacher took a whole hour.
This is absolute genius and beauty! Thank you so much for sharing this gem Sir. love your videos
Thank you for the very nice comment!
Its 9 pm and this made my day
Love it. Like your clear informative shorts
That's brilliant. Love it...
Really confused me when he kept saying "equals two" instead of just "equals" until I realized it was "Equals to"
Thanks for making this video for others to see and understand reapeating decimals.This was very easy to understand
I just wanna say you're a really great teacher, sir. Your videos are exciting and easy to understand.
Thank You Mr.H i have learnet this when i was 11 grade but i forgot it now i am a university student freshman thank you for the remainder
this video really helped me. explained it alot better than the book
Great teacher.
I never learned this. That's actually really cool.
How exciting. I remember sitting in class 50 years ago learning this. I never needed it again. Damn.
This is a such a random treat to pop up on my feed.
I love the whole approach.
That's so cool! Didn't know you could do it like that.
I love the fact that I can just do this on the calculator, meaning that I don't HAVE to be able to do this, but I GET to do it and have fun with it. Thank you for all the cool methods sir, it really makes maths fun.
My reaction: 😱🤯🥰
OMGosh!
My mind's blown!
I love this guy! I can now teach this to my boys!! TY TY TY!!!
Thank you~
Just coded this to have it working for everything thanks to this
A faster trick is to take the repeating part and put it over the same number of 9s.
For example 0.123123123 = 123/999.
But I didn't know how to prove this trick so thanks for the video!
I wish I had this guy as a teacher way back in HS
That's exactly how I was taught this very same lesson in 1979. Nowadays kids don't even learn this in 5th grade :(
I majored in math and physics. Usually the weakest math majors ended up teaching at the high school level. In order to work in the math lab you had to pass a test of 5 or six word problems. It was sad that a large percentage if senior teaching majors couldn't even work rudimentary problems. To make matters worse, at math departments across the country, the weakest teachers end up teaching the students that are the farthest behind.
Glad to say I figured it out before I even clicked on the short lol
Fun Fact: Any repeating decimal such as 0.22222 would be (x over 9) such as 2/9, and 0.444444444 would be 4/9.
Well done professor
mr H is my new favorite math teacher!
So basically the repeating number over 9. Got it.
As a person who struggle at math so badly i started to dislike it, I started to no longer hate it
Well done master.I enjoy your video.
Glad you enjoyed it!
That's actually handy to know, thanks!
Love & Support 💪💕 for u
love from India 🇮🇳.
I'm gonna slowly regain my math skills due to this channel
I've learnt competitive tricks to do this but never got "explained" the logic of why they work
I don’t remember any of this. Thanks for the refresher course ⭐️
Any time!
love the sound of your chalk :-)
Also worth noting that you don't have to multiply by 10 each time, the thing is, you have to get one part of the number out of the decimel, so for example if u were to convert 0.265265265... you should multiply by 1000 and continue the calculation....
I love the fact that when to try to get a fraction for 0.99999....... it becomes
x = 0.99..
10x = 9.9999....
So 9x = 9.9999 - 0.999 = 9
So 9x = 9
So x = 9/9 = 1
So basically it gives 0.9999999 = 1
To find the digit sum of any number faster, strike out all 9s, and the remaining number would be the digit sum. E.g. 1) say for 456, strike out 4 and 5, because their total is 9. The remainder is 6, so 6 is the digit sum. 2) say for 879, strike out 9, remaining is 87, take out 1 from 7, add to 8 to get 9, which can be strike off, final number remaining is 6 (7 - 1). This striking out all 9s technique can be used for any number to find the digit sums. Thanks to Vedic Maths!
exactly a way to compute geometric series.
Отличный преподаватель. Я совсем не понимаю что он говорит, но понял как он нашел ответ. Это на сколько просто, что мне стыдно, что я сам до этого не дошел
I remember doing that in my first Calculus Class, its so nice
Such a brilliant Maths Teacher ❤
They always taught me to write 0,5 with the periodic line on the 5, then to rewrite all without the stating zero and the periodic fives, subtract all that isnt part of the period (in this case it can be avoided), then it becomes 5, just add an 9 at denominator (one for every periodic digit, so only 1 because it is only the 5 here)
ones like this are actually helpful in my life. dunno why I never learned this out of all the math I did learn
That's awesome. I love it....
I remember this explanation when talking about repeating numbers during middle school.
Amazing absolutely brilliant
Bro made math 0.5x easier 💀
I love this! Thank you!
❤love this!!!!!!
Genius is the natural ability to see things that others don't. If one doesn't have that natural ability then one has to focus and work better to become a "genius".
Learned this the other day, I was surprised by how simple it is lol
WOW. This is great. Thank you.
very good and easy to remember and understand.
very simple to remember the idea to multiply. so you align the digits of the repeting part and you can eliminate it by subtraction.
in the school they taught me a very hard to remember fraction rule
This is the same method used in the simplest proof of 0.99999... = 1. Just like he showed that 0.55555... = 5/9, you use the same procedure to show that 0.99999... = 9/9, which is just 1.
Bah bro. That’s disgusting. I love this one
Fantastic Sir.
I really miss my school days 😭😭 my ears crave for that magical chalk sound ❤
It also helps knowing that the only way to get a number to repeat is by dividing by 9. This is also the reason why 0.99 (repeating) is equal to 1. To get 0.99 (repeating), you would have to divide 9/9, and that's just 1.
I'm like "oh yeah, 0.NNNN repeating is N/9" but this trick is really cool!
Oml this topic came up so much in the shsat and now I’m getting these vids
Thank you for your videos. They remind me of math classes I took in high school. Truth here. A few of us hs-students would go to school an hour early and work math problems--this was at 7am. Our math instructor always wore a suit and tie. Most of this would seem a little odd these days. Believe it or not we thought math was fun - no calculators allowed 😆 To this day when dealing with simple transactions I can beat the computer response when shopping. People give me a puzzled look when I tell them the answer. My policy is stay humble and be an old nerd.
Also I was the only girl there. 😮😊
In school I had learned only the result of this process. That is, whenever you have zero-point-repeating-numbers, the answer is one of those repeating sequences divided by as many nines as there are digits.
That is, 0.111111... is 1/9; 0.121212... is 12/99; 0.123123 is 123/999, and so on. But we never went over the reason _why_ this works. And that's worth learning, because studying math isn't meant to be just learning a series of rules. It's about understanding numbers and how to play with them. We learn existing solutions to existing problems so that we can develop new solutions to new problems. This is especially true today, when we're all carrying a very sophisticated calculator and mathematical analyzer in our pockets. There's not really any merit in learning a bunch of processes if the machine in our pockets is going to get the answer more quickly and with fewer errors. Basically, we have to ask ourselves, what is the point of still learning math these days? And if learning math is just about studying the programmatic processes that our meat-brains do so slowly, the answer would kind of have to be "Eгг".
He makes maths entertaining.
Great stuff.
Ahh the classic subtract from the entire equation I didn’t know about. 😂
Formula for infinite geometric series can also convert it into fraction although the method explained here is very simple.
That formula is pretty much what allows us to do this. But it’s much easier just taking this shortcut.
@@Daniel31216 it's not a shortcut
@@agnidas5816 It is though. We can only do this because of calculus, so this is just an easier way of doing it.
@@Daniel31216
How would u do it with calculus?
@@WomenCallYouMoid Like OP said, it can be done with geometric series.
Also that's a neat explanation of why 0.999... = 1
Yup!
now thts what i call number sense !👍🏿❤
.99999999999999=1
mr h. thank you for your help with math
Cool trick did not know this one always used intuition
cant believe how i forgot the sound of the chalk written on the board.
The Teacher is a Genius.
If your good at it, do you think you could also make science videos like these?
Impressive!
May ALLAH blesss u and gives u more knowledge
This is genious! 👏
Good way to compute 🎉🎉🎉
Today I got the explanation , thank you so much Sir
Great 👍
Now I understand how do you it thank you a lot 🙏🏻
No problem 👍
native teacher thank you alot🙏.
Basically any single digit number except 9 when divided by 9 will get a repeating decimal
This is an example of a single digit repeating. So this method can be used exactly nine times. Use the same principle to × 100 for 2 digits, 1000 for 3, etc.
Lmao now I don’t have to do a geometric series representation of it
This is just a short cut of that.
pre-calc moment
How would you do a geometric series for one number? Genuine question
Excellent
Mind blown 🤯