Incorrect reasoning: she said that 47 is greater than 5. But 5 is a whole number, therefore Alex must've ran 5 miles, which is much greater than Christy's.
How to correct her reasoning: She can correct her reasoning by knowing that 47/100 is not not a whole number. 5 miles is equal to saying 500/100, and that is much larger than 47/100.
47/100 < 5
