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
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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
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 ^^
why would you want to do this? just asking.
mmk ta +rep
LOL
wuttttttt did this entire thread just say.
ive been taught you can't have a decimal in a fraction?
ive never been taught this and i do a-level maths :S
it's not like it really matters all that much anyway.
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!