mathsmathsmaths +rep

[ecstasy]

recurring decimals to fractions

i can do the simple ones e.g 0.3232323232... but I've completely forgot how I'd do something like 0.132323232...

so say if i had to change 0.1323232... to a fraction, how would I do it? taaa x

[Matthew]

ahh i remember doing this now xDD

to do this, i would do:

0.1323232 x 100 = 13.232323
then subtract

Then divide both sides by 99

100x = 13.232323 ...
- x = 0.1323232 ...
_____________________
99x = 13.1

x = 13.1/99

SO 0.1232323 =
13.1
_______
99



sorry if you dont understand LOL (its how IVE been taught)






EDIT: basically, multiply the recurring decimal (we'll call it w) by a number (if 1 digit recurs, by 10; if 2 digits recur, by 100 etc)(we'll call it y)
(Set it out as i have above, i.e
100x = (wx100)
- x = w)

Then subtract all (y-w, and 100x-x)

you will then get 99x = (y-w)
And so you simply re-arrange the equation to find 1x (divide each side of the = by 99)

SO, x = (y-w) / 99

Simple <3

It seems so long winded, but it really is ^^

[kk.]

ahh i remember doing this now xDD

to do this, i would do:

0.1323232 x 100 = 13.232323
then subtract

Then divide both sides by 99

100x = 13.232323 ...
- x = 0.1323232 ...
_____________________
99x = 13.1

x = 13.1/99

SO 0.1232323 =
13.1
_______
99



sorry if you dont understand LOL (its how IVE been taught)






EDIT: basically, multiply the recurring decimal (we'll call it w) by a number (if 1 digit recurs, by 10; if 2 digits recur, by 100 etc)(we'll call it y)
(Set it out as i have above, i.e
100x = (wx100)
- x = w)

Then subtract all (y-w, and 100x-x)

you will then get 99x = (y-w)
And so you simply re-arrange the equation to find 1x (divide each side of the = by 99)

SO, x = (y-w) / 99

Simple <3

It seems so long winded, but it really is ^^

This, but youre best to set it out like:

let x = 0.13232323...

100x = 13.232323...

100x - x = 13.232323 - 0.13232323

99x = 13.1

x = 13.1/99

[Matthew]

This, but youre best to set it out like:

let x = 0.13232323...

100x = 13.232323...

100x - x = 13.232323 - 0.13232323

99x = 13.1

x = 13.1/99
isnt this exactly how i set it out just the other way up?
and surely mine is easier because the larger number is on top?
idk, i tried my best to make it clear xDDD
(much easier when the writing is in your book, and not on a pc screen :P)

[alexxxxx]

why would you want to do this? just asking.

[kk.]

isnt this exactly how i set it out just the other way up?
and surely mine is easier because the larger number is on top?
idk, i tried my best to make it clear xDDD
(much easier when the writing is in your book, and not on a pc screen :P)

it is basically what you did yes, but following yours was confusing, and it looks like the x and 100x appeared from thin air :P

[ecstasy]

mmk ta +rep

[Swastika]

LOL
wuttttttt did this entire thread just say.

[dbgtz]

ive been taught you can't have a decimal in a fraction?

[Matthew]

ive been taught you can't have a decimal in a fraction?
you can't no, but i left out changing 13.1/99 to 131/990 because it seemed kinda needless... but yeah i've been taught that aswell :)

[MattFr]

you can't no, but i left out changing 13.1/99 to 131/990 because it seemed kinda needless... but yeah i've been taught that aswell :)
It's not pointless considering 13.1/99 would get you no marks :)

[kk.]

ive been taught you can't have a decimal in a fraction?

its how you left it anyway.. but no, you shouldnt have decimals in fractions.

[alexxxxx]

ive never been taught this and i do a-level maths :S

it's not like it really matters all that much anyway.

[kk.]

ive never been taught this and i do a-level maths :S

it's not like it really matters all that much anyway.

ive never had to use it in a level maths :P, nor on further maths lol

[Soka]

for ones such as 0.1313131313 your method is correct... let x = 0.1313..., then 100x = 13.13... so 99x = 13, there x = 13/99
the key is to make sure you multiply x by the period (size) of the recurring part. so in above case 0.131313 obviously has repeating period 2 (as 13 is two digits). so you'd mutiply by 10^2 = 100. if it was 0.134134134, you'd multiply by 10^3 = 1000, then 999x.. then x=134/999.

for the other one x = 0.132323232, where you have a non-recurring part at the beginning first multiply by 10^n where n is the period of the non recurring part.. so in this case it is period 1 (1 has one digit)... so 10x = 1.32.... then carry on same as previous part.. so multiply this by 10^2 = 100.. so 1000x = 132.32...
then we can say 990x = 131, then x = 131/990, as a fraction.

i think alot of the guys above where missing out the step in bold.. so was not getting a fraction as the first answer ! so they had the right answer from multiplying 13.1/99 by 10, but this isn't the correct method and i don't think you'd get the marks... although i don't know at GCSE/A Level you might.
hope this helps if it makes sense.

[Matthew]

It's not pointless considering 13.1/99 would get you no marks :)
what i meant is that i assumed he would change the fraction to 131/990 himself :P

[Matthew]

for ones such as 0.1313131313 your method is correct... let x = 0.1313..., then 100x = 13.13... so 99x = 13, there x = 13/99
the key is to make sure you multiply x by the period (size) of the recurring part. so in above case 0.131313 obviously has repeating period 2 (as 13 is two digits). so you'd mutiply by 10^2 = 100. if it was 0.134134134, you'd multiply by 10^3 = 1000, then 999x.. then x=134/999.

for the other one x = 0.132323232, where you have a non-recurring part at the beginning first multiply by 10^n where n is the period of the non recurring part.. so in this case it is period 1 (1 has one digit)... so 10x = 1.32.... then carry on same as previous part.. so multiply this by 10^2 = 100.. so 1000x = 132.32...
then we can say 990x = 131, then x = 131/990, as a fraction.

i think alot of the guys above where missing out the step in bold.. so was not getting a fraction as the first answer ! so they had the right answer from multiplying 13.1/99 by 10, but this isn't the correct method and i don't think you'd get the marks... although i don't know at GCSE/A Level you might.
hope this helps if it makes sense.
its exactly how ive been taught at a GCSE level, so yeah im not sure for A level :P

what ive been taught is that you multiply it by 10x(the number of recurring numbers there are). so in 0.13232 there are 2 recurring decimals, therefore we times it by 100 :)



EDIT: sorry for double post, it didnt occur to me at the time.

Edited by Okapia (Forum Moderator) Please try to avoid double posting within the 15 minutes editing time. Thanks!