Algebra
posted by HLD on .
Can someone explain how you could convert a repeating, nonterminating decimal to a fraction?
Thanks. :)

I will illustrate with an example
4.5676767...
let's just work on the decimal .5676767...
let x = .5676767...
multiply by 100 , (because 2 digits repeat, so 2 zeros in 100)
100x = 56.7676767
subtract ...
99x = 56.2
x = 56.2/99 = 562/990 = 281/495
so 4.5676767.. = 4 281/495 or 2261/495
quick way:
for the numerator,
>write down all the digits to the end of the first repeat  567, subtract the nonrepeating digits
5675 = 562
for the denominator, for one complete period, we have 1 leading nonrepeating followed by 2 repeating ,so
put down a 9 for each repeating digit (so 2 9's) followed by a 0 for each nonrepeating digit, (so one 0)
or 990
.567676767... = 562/990 = 281/495
e.g. .34123123123...
 (34123  34)/99900 = 34089/99900 
how are you people