Write the recurring decimal 0.ababab as a fraction. (10 points)

A) a + b/ 99
B) a * b / 99
C) 10b + a/ 99
D) 10a + b/ 99

1 answer

any recurring set of n digits abc... is
(abc...)/(999...)
where there are the same number of digits top and bottom. To see this, do

x = 0.ababab...
100x = ab.ababab...
now subtract to get
99x = ab
x = ab/99 = (10a+b)/99
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