.2727… = what fraction? MOST will NOT Be Able to FIGURE OUT! 

The general rule of thumb in base 10 is to put the repeating part (In this case, it is "27") over all 9s. So, in this case, you would have 27/99. This would eventually reduce to 3/11.

"Encourage people not to give up on math." Bless you, sir!

For some reason, we, (1970's) were NEVER taught this in High School. I had to learn this on my own. I did it algebraically. If it is 1 decimal repeating, use 9, 2 decimal use 99, 3 decimal 999 .... etc. And yes, I figured this out the way you show it in this fine video.

For sure in the 60’s, we definitely did Not learn this! Thank you for an interesting video! Linda

Nice review! I haven’t seen that since high school and didn’t remember it.

It would be clearer if you always put a horizontal bar over the last "27" in all cases that it applies. Then you wouldn't have to keep explaining that it repeats.

This was a very neat trick. I solved it by brute force myself. I figured that the result was just a little more than 1/4, so I starting adding 1 to the numerator and dividing the bigger numerator with (4 * numerator) - 1). So 1/4=0.25. 2/7=0.2857. 3/11=0.272727 and Bingo

Interesting! I don't remember learning this in school,

Yes I can... x = 0.2727272727.... then 100x = 27.272727272727... So 100x - x = 99x = 27 and resulting in a nice fraction x = 27/99 = 3/11

NOT ABOUT THIS. Other sites say that PEMDAS does not work for all . . . I understand your voice and presentation. . . . thanks

Thank you

This is 0.27 recurring. 2 recurring decimals for every decimal ÷9. Do the answer is 27/99 =3/11. Simple. Didn't take me ages

3/11. slightly bigger than1/4, less then 1/3. Did a few trial and errors to see the pattern between changing the numerator and denominator by a digit to see where the pattern goes. presto, 3/11. Now I'll see how it was meant to be done.

I defaulted to an approximation (same as done with pi). ~27/100. There's my fraction.

The method shown does work but there's a much easier method if there are no non repeating digits before the repeating digits, as here. For the numerator, write down the first string of repeating digits. Here that's 27. For the denominator, write as many nines as the number of digits in the numerator. There are two digits in the numerator so 99 is the denominator. 27/99 is 3/11. Again, if there ARE non repeating digits before the repeating digits, the solution is more complex because you would need to create a second fraction using the non repeating digits (using different rules) and then add the two fractions. Example: .037037. The numerator is 37 and the denominator is 999 since there are three digits in 037. 37/999 is 1/27. Using this method, .272727 can be converted to a fraction mentally.

This is great! So if I understand, take the repeating portion of the decimal, move the decimal point to the right - that’s the numerator - now in the denominator, put a 9 under each digit above (16:46). Shouldn’t this have a name, like “John’s Rule of Nines?”

Very interesting, I was never aware of this trick.

3/11, worked it out before opening the video, so I'll be fascinated to see what your methods was. I did iit like this, 27/100, so just a little over 1/4. You need a repeating pattern and using integers, I went next up to 3/11 was the first try. I am sure that is not scientific though! Best wishes from George. PS: Not taught this, and was born in 1961 in England.

Just when I thougth I knew what to do with a one step linear equation you come up with this. :( Great! :(

This was a wonderful method and I am certain I was never shown this in school (1960's). I am also certain that I would never have been able to figure out this method on my own. But I did get the answer a different way. First, I assumed that since only the first two decimal places repeat, then the numerator and denominator are going to be small numbers. (I'm not sure if that assumption is always correct.) Then I took the fact that .27 is a little bit larger than 1/4. So the numerator and denominator are going to be only one or two digits, and I'll try fractions which are a little bit more than 1/4. Let's increase the N and D by 1. That's 2/8 (which = 1/4). Now, a little bit larger than 2/8 is 2/7. That didn't work. So let's add one more to the D and N to get 3/12. Now, a little bit more than 3/12 is 3/11. That turned out to be right. That worked with .272727..., but I'm not sure if it would work so well with any other two-digit repeating decimal. Edit: I've been playing around with this and discovered that ALL fractions with 11 as a denominator are two-digit repeating decimals! And there is no other denominator which does that. Also, each denominator has its own pattern of repeating decimals. And if you go to twice the denominator (say from 7 to 14) then that decimal will have the same number of repeating decimal places, only starting with the second decimal place, not the first (unless the fraction reduces). For example, 3/22 is .136363636.... 5/7 is .714285714285... but 5/14 is .3571428571428.... All 7ths have a six digit repeating string, and amazingly, it's the same six digits in the same order, only beginning with a different digit depending on the numerator! 1/7 is .142857142857... 2/7 is .285714285714... 3/7 is .428571428571... WOW! (To which, the math gods would say, "Well, duh, it does that because...".)

Very nice trick. I think I learn something else a few years ago... I just can't remember. :)

That is an interesting and clever trick. But I solved it in a different way. x = 0.27272727.. It was said that you could use a calculator, so I used it to get: 1/x = 3.66666666667 and I can imediately recognise the .6666666667 part as related to 2/3 So then 3 x (1/x) = 11 or 3/x = 11 -> x = 3/11 and my calculator checked that as correct A different denominator may not have been recognised so your method is better, thanks.

I used a slide rule.

this was a tough one.

Hey i learnt something. Mr RU-vid Mathsman should put a bar over himself when he keeps repeating himself

got it. the fraction conversion is 27/99 or 3/11 thanks for the fun

pretty easy just realize this is only for numbers that can be expressed as a fraction.

I learned that in the 8th grade. I can't believe i got this answer in seconds. Wow!

Now, a more interesting problem will be to figure out 1/12. This is because 1/12 = 0.083333333 ... This will involve multiple techniques, including what you demonstrate in this video.

I've seen that before. Something over 11 I think. Yep. 3/11.

I would not want to I What would be the reason?

27／99=3／11

Funny and insane, but good. It looks familiar to me. Very clever.

I never learned this. I'm sure of that. I don't think anybody ever tried to teach it to me, either. Even in college algebra.

3/11 in my head.

Instantly recognised. How about 0.428571 recurring?

27/100

27/99 = 3/11

3/11

Why not teach students logical short-circuit and very easy logical steps. If we have after decimal points only the period of the periodic fraction the student already have the numerator. The denominator has as much nine's as the number of digits in the numerator. That's it. 0.(27) = 27/99 0.(4) = 4/9 0.(15) = 15 /99 0.(123) = 123/999 and so on.

3/11. Did it by trying to and fail

Most will never need to be able to figure this out...

My scientific calculator on WIndows 10 tells me that 7/31 = 0.22580645161290322580645161290323 Repeating unit is 225806451612903. How would you approach that?

This is the same technique that proves that 0.999... is equal to 1

27/99 = 0.272727....

What about 0.166666... = 1/6. How to you get that type?

1/x button.

1/000000004

Factor the 27. Its got to be 9 or 3

explanation went on too long - usually your slow and careful discussion was helpful - but this time it was just dragging it out.

2/27

27272727/100000000

27/99

Maybe 27/99...

Oh dear John.This very same technique was used to prove 0.999.... =1 (which is wrong). Once you operate on a recurring decimal number ie x or / 10, 100, 1000 etc, you create a shift of digits in an infinite series which is no longer equal to your original series (even though both are still infinite). Subtle, but true I'm afraid......0.272727...is irrational.. As for using a calculator which doesn't have an infinite memory to prove your theory is unforgivable Try dividing 3 by 11 you do get 0.272727, but multiply this by 2 , and you'll find an error ie 0.5454......44

Most boring explanation I have ever listened to 14:52

Love the way you work it all out but the explanation is far too long. I'm unsubscribing only because I waist too much time. Could be learning this a lot faster.....

1/3.666666703

The correct answer is 2.72727272727..../10 It's that simple.

Thank you

27/100

3/11

3/11