# Converting recurring decimals to fractions new formula

Okay so the name may be bigging it up however i found something in my maths class today that i dont think has previously been published or at least ive never been taught it, it makes converting reacuring decemals alot quicker
I know about the over 9 rule however acording to my maths teacher this rule is only possible if the recurring number(s) come directly after the decimal point and not if there is a non reacuring number directly after the decimal point
I apologise if thats hard to understand not very good at explainging things via typing and i also want to stress that i have no idea if this is a thing alrady or not and if it is its handy and will help with my exams so a plus if its not then i guess i think it would be handy for people to know.
Please no negative stuck up replys i guess what im asking is is it possible to use the over 9 rule with a reacurring decimal that has a non reacuring number directly after the decimal poing eg 0.2(nr)25(both reacuring •) i will post the "theory" if some one does not reply with it saying this is alrady a thing soz m8

mfb
Mentor
0.225 = 1/10 * 2.25 = 1/10 (2+25/99) where bold means repeating.
No magic, very simple algebra. Way too simple for a publication.

Okay answer appreciated however and this is according to my maths teacher my answer was correct 223/990 and i will post the theory just to show you but it was along the lines of
You take the non recurring number(s) in this case 2 then you take that number away from the whole number 225 leaving you with 223 you then place this on top and underneath you put one 9 for every recurring number and a zero for every non recurring number, so on top you have 223 and at bottom you have 990 one nine for the recurring 2 and one for the reoccurring 5 and one zero for the non recurring 2
This enabled me to do them all quicker than how we were shown which is why i thought it may be of some use ,its also worth noting that the formula does work for all the questions including ones such as 1.2(25) (brackets=recurring)
I appreciate that this may just be simple that just thought it was quite a handy thing to know like, however im 15 in secondary school and wether its of any use or not is beyond me

mfb
Mentor
There is no practical application of making those transformations manually, and a computer doesn't care (computers store numbers differently).
It works, yes, in a similar way to the calculation in post 2, just a bit faster.

Yes but practical application or not we are still taught it in school and require to be able to do so to pass our exams and if this way works faster and easier than the standard way then i just thought it would make sense for people to use it,as for computers not caring ok agreed however i could use a calculator to do most mathimatcal sums in our non calculator test in a matter of minutes but we are not allowed to use them so this is a manual form of doing the sum the fact that you have just stated there is no need for a way of manualy doing sums is wrong thats like saying no one needs to understand maths because they can use a calculator in every practical element of life, so there is no point in me doing maths at school? There is no point in peoples degrees and things in maths as a calculator can do it better ? No obliviously there is a point to being able to do manual maths and any way of making life easier is a good thing right

Mark44
Mentor
Yes but practical application or not we are still taught it in school and require to be able to do so to pass our exams and if this way works faster and easier than the standard way then i just thought it would make sense for people to use it,as for computers not caring ok agreed however i could use a calculator to do most mathimatcal sums in our non calculator test in a matter of minutes but we are not allowed to use them so this is a manual form of doing the sum the fact that you have just stated there is no need for a way of manualy doing sums is wrong thats like saying no one needs to understand maths because they can use a calculator in every practical element of life, so there is no point in me doing maths at school? There is no point in peoples degrees and things in maths as a calculator can do it better ?
Off-topic, but the above is a very long sentence. Have you learned about the use of the period (.) yet?

Mark44
Mentor
Okay answer appreciated however and this is according to my maths teacher my answer was correct 223/990 and i will post the theory just to show you but it was along the lines of
You take the non recurring number(s) in this case 2 then you take that number away from the whole number 225 leaving you with 223 you then place this on top and underneath you put one 9 for every recurring number and a zero for every non recurring number, so on top you have 223 and at bottom you have 990 one nine for the recurring 2 and one for the reoccurring 5 and one zero for the non recurring 2
This enabled me to do them all quicker than how we were shown which is why i thought it may be of some use ,its also worth noting that the formula does work for all the questions including ones such as 1.2(25) (brackets=recurring)
I appreciate that this may just be simple that just thought it was quite a handy thing to know like, however im 15 in secondary school and wether its of any use or not is beyond me
I am more interested in why this works than I am in the process itself. Can you come up with an explanation of why this works?

mfb
Mentor
@Charliepic: The point of those exercises is to understand fractions, the decimal representation and so on. In particular, I think the more standard steps show more clearly what is happening.
If you understand why your method works (and not just by accident) then you can move on to the next topic anyway.

@Mark44: are you asking that in general, or specifically Charliepic?

Mark44
Mentor
@Mark44: are you asking that in general, or specifically Charliepic?
Specifically Charliepic. I quoted what he wrote, which I thought would make it clear my comment was addressed to him.

mfb
Mentor
I just noted that this method has an ugly extra rule for numbers like 0.3412, where bold means repeating as above. You can still use it, but you need an additional rule to handle the carry as the obvious way does not work.

Ymm im in midde of my exams so havent had a chance to look on hear sorry ymm il have a look as to how this works as for the number you put mfb could you place the reacuring in brakets so i can see no formating on my phone...[emoji58] - as for bad grammer il just apologies and leave it at that

mfb
Mentor
0.34(12)
0.34121212121212....
You could have quoted my post to see the formatting I guess.

Off topic mfb you come across as a make every situation awkward t*** you could change that, i guess.
On topic i fail to see how that does not simply become
3412-34 = 3378
3378/9900

3378/9900= 0.34(12)

Please explain this extra rule because i did not use one and got a correct answer i get the feeling you dont like this but you dont need to be a dick

Specifically Charliepic. I quoted what he wrote, which I thought would make it clear my comment was addressed to him.
Mark44 i think this works because the original method would be to times the number so that the repeat started directly after the decimal point eg.

0.341212121212 * 100 = 34.12121212

And then you would do the same but so one repeat is before the point eg.

0.341212121212*10000 = 3412.12121212

Then you take away the first number from the second leaving you with

9900 X= 3412.12121212-34.12121212 = 3378
X=3378/9900

My method is simply doing the minuses without the need to multiply hope this helps to understand [emoji4]

Sorry mfb post #13 was meant for mark44 post #15 was for you

mfb
Mentor
Hmm it works without a special rule, right. My mistake.

[emoji111]️[emoji263]