The answer depends on what string is repeating. It is not clear from the question whether the recurring fraction is meant to be 0.580580580... or 0.5808080...
0.580 can be expressed as the repeating decimal 580/1000. To convert it to a repeating fraction, you can find the least common multiple of the denominator (1000) and the digits that repeat (580). In this case, the least common multiple is 2000. You can then express the repeating decimal as a fraction with a numerator of the repeating digits (580) and a denominator of the least common multiple of the repeating digits and the original denominator (2000).
so,
0.580 = 580/1000 = 580/2000
0.580 as a repeated fraction is a nonsense. Do you mean what is the fraction 0.580580.... as a repeated decimal.
NB To indicate that decimals repeat to infinity they are written as ' 0.580580...' It is normal mathematical practise to write three full stops/periods to indicate repetition to infinity.
0.580 as a fraction is 0.580/ 1.000 = 580/1000 cancel down by '10' hence
58/100. Cancel down again by '2' . hence = 29/50 This will not cancel any further because '29' is a Prime number and '50' is NOT a multiple of '29'.
To convert 0.580580... to a fraction ;-
LetP = 0.580580....
Hence #1000P = 580.580580....
Subtract
1000P - P => 999p = 580 Note the repeating decimals subtract to zero.
Hence P = 580/999 This will not cancel down any further.
0.453 repeated as a fraction = 453/999
.23 repeated as a fraction is 23/99
The number .475 repeated as a fraction would be 475/999.
If it's only the '4' that's repeated, then the fraction is 2/45 . If the '.04' is repeated, then the fraction is 4/99 .
0.3 is 3/10 as a fraction. It is NOT '1/3' 0.3333333...... repeated to infinity is 1/3
It is 1 2/3.
5/3
It is 40/9.
6/7
213/999
It is 26/9.
It is 7/9.