What fraction = .272727272727…? Many, never learned this! 

You are right! I never learned this. Thank you for the lesson.

Another way of doing this is treating 0.2727272727 (it goes on and on) as a geometric series with first term 27/100 and common ratio 1/100, since 0.272727...=27/(10)^2 + 27/(10)^4 + 27/(10)^6+... . The series converges since -1

0.272727... = 27/99 For any repeating decimal number... 1) Take the repeating part (in this case, it's 27) 2) Count the number of digits in the repeating part (in this case, "27" is 2 digits) 3) Create a number made up of that number of digits of "9"s (in this case, 2 "9"s: "99") 4) Divide the repeating part (27) by the "9"s (99), so: 27/99 5) If the decimal number was 0.472147214721..., the fraction would be: 4721/9999 If you want (need) to reduce it, it would be: 27 3 ---- = ---- 99 11

Great refresher. Brushed the rust on a skill from the past. Thanks for sharing and keep on doing what you are doing. You are helping unknown numbers become more efficient

Something else many never learned...the bar above the digits is called a vinculum.

Once I saw it has .090909 as a factor, I new the denominator was 11 and reasoned that the answer was 3/11.

This is new to me, I did get the correct answer fairly quickly by trial and error but not by the objective method presented here.

My route was to find the reciprocal of 0.2727, which gave an improper fraction 1/(3 2/3). I multiplied the result by 3, to give a proper fraction 3/(9+2) or 3/11. I do remember being taught your route in junior school in the late 70's / early 80's.

you're correct....never learned this. thanks for the lesson.

The repeating part (27) over the same digit length of nines (99). So 0.28571428... = 285714/999999 = 2/7 I always taught this. The trouble is, there are many people reacting maths who themselves are poor at maths.

I reasoned it out. Repeating decimals will have an odd denominator, so I decided to math-ish it. 27/100 (I rounded), is pretty close to 27/99 and simplified to 3/11. Thank you so much for this review. I teach remediation in Jr High and it amazes my students that I do your math problems for review and fun.

An interesting technique, not something that was taught here in the UK 50 or so years ago (if I remember correctly😊}

this could've been a 3 minute video.

took the inverse of decimal (1/x) and got 3.666~.....which is 3 & 2/3. which is 11/3 and inverted that. Also, 3/10 is .30 and 3/12 is .25, and knowing 3/11 is between them and anything divided by 11 has repeating digits, must be 3/11.

That is so neat! Thanks Mr RU-vid Math Man!

This is great.

fractions thru twelfths are pretty easy to remember

3.14 is actually a pretty good approximation of pi. It is low by 0.05%, certainly close enough for many things.

100s -s = 99 s = 27. Solve for s.

Excellent, I forgot this.

This is proof that mathematicians can make any rule about numbers even if the rule is impossible. Let's call them mathematical loopholes. Like 0 and infinity.

3/11 = .272727..... I learned that in the 4th grade. Methods are unnecessary in math if you learn things the first time you do the math. It takes longer your way.

27/99 which is 3/11

Cool method. Don't remember if I learned it or not 😉

Over ten minutes before starting on the solution and then interrupting it by an ad.

Calculus?

It is

pi is a fraction 22/7

I understand the how but not the why.

.272727 x 11 = 3 3/11 = .272727

27/99

Clever. I brute forced it in Excel by multiplying 0.27272727 by integers from 5 to 15. 11 * 0.27272727 rounds to 3 at 4 significant digits, so 3/11

Roughly 1/3

10 minutes blabla until you start to explain the solution, thats way to much!

3/11

Looks like 3/11

You are a good teacher, but unfortunately you waste student’s time by talking too much. Shame on you.

too muck talking i fell asleep zzzzzzzzzzzzzzzzzzzzzzzz

27/99

27/99