Question

Can someone explain how you could convert a repeating, nonterminating decimal to a fraction?

Thanks. :)

Answer 1

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 non-repeating digits
567-5 = 562
for the denominator, for one complete period, we have 1 leading non-repeating followed by 2 repeating ,so
put down a 9 for each repeating digit (so 2 9's) followed by a 0 for each non-repeating digit, (so one 0)
or 990

.567676767... = 562/990 = 281/495

e.g. .34123123123...
- (34123 - 34)/99900 = 34089/99900

Answer 2

how are you people