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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 = 29/50 = 58/100 = 116/200 = 232/400 = 464/800 = 928/1600 = 1856/3200 = 3712/6400 = 7424/12800 = etc.
The answer depends on what string is repeating.
As a fraction, the answer is = 29/50.
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