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let x=.5 repeating. because .5 repeating has one digit repeating, mulitply each side of x=.5 repeating by 10 to the first power, or 10. then 10x=5.55 repeating. subtract one x from 10x, so since each x is .5 repeating, 5.55 repeating minus .5 repeating is 5. that means 9x=5. then its x=9/5, which is your answer. if possible, simplify. so the answer is .5555 repeating is equivalent to the fraction 9/5.
Doesn't 9/5 = 1.8? I mean if you use your calculator to do the check the math it doesn't make sense that a top-heavy fraction can be less than one, does it not?
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