Like this. You call your number "x", and write:x = 0.435435... (equation 1)
1000x = 435.435435... (equation 2)
Then, you subtract equation 1 from equation 2, and solve for "x". This will give you "x" as a fraction.
Note: The factor 1000 was chosen because the period (number of repeating digits) is 3, and 1000 has 3 zeros.
1000x = 435.435435
x = 0.435435
Subtract them.
999x = 435
x = 435/999 or 145/333
0.6666 repeating = 2/3
123/999
7.11111...=7 1/9 or 64/9
0.161616... = 16/99 which cannot be simplified.
1.'19' repeating '19' as a fraction is 118/99
0.2 a repeating decimal into a fraction = 2/9
0.6666 repeating = 2/3
0.999 repeating = 1 (the integer).
If you convert repeating decimals into a fraction, you see that the repeating decimals are rational.
sexx
Just have a go.
56/99
It is 2/3.
123/999
998/999
998/999
0.555555555... = 5/9