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 D

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

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

[kk.]

ahh i remember doing this now D

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

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 DD
(much easier when the writing is in your book, and not on a pc screen )

[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 DD
(much easier when the writing is in your book, and not on a pc screen )

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

[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