Problem: When the repeating decimal 0.363636 . . is written in simplest fractional form, the sum of the numerator and denominator is:
Answer Choices:
A. 15
B. 45
C. 114
D. 135
E. 150
Solution:
0.363636…=10236+10436+…=1−1/10236/102=9936=114, so that the correct answer is (A).
Let F=0.363636…100 F=36.363636…99 F=36 F=9936=114