Posted by Babiinoob on Thursday, October 6, 2011 at 6:51pm.
I don't know which method you use, but here is one of the more common ways ....
let x = 3.230423042304...
multiply by 10000 , (there are 4 digits in the repeating loop, so a zero for each repeating digit)
10000x = 32304.23042304..
subtract them
9999x = 32301
x = 32301/9999 = 3589/1111
shortcut:
look only at the decimal.
for the numerator write down all the digits to the end of the repeating loop --- 2304
subtract all those digits that don't repeat -- none to subtract
for the denominator:
write down a 9 for each of the repeating digits -- 9999
add a zero for each non-repeating digit -- no zeros to add
so 3.230423042304... = 3 + 2304/9999 = 32301/9999 = 3589/1111
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