Asked by Lia
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
A) a + b/ 99
B) a * b / 99
C) 10b + a/ 99
D) 10a + b/ 99
Answers
Answered by
oobleck
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
(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