Bunuel wrote:

Which of the following fractions is equal to the repeating decimal 0.3636...?

A. 1/275

B. 2/55

C. 4/99

D. 4/11

E. 4/9

We see that 0.3636 is between 1/3 and 2/5.

Looking at the answer choices 1/275. 2/55 and 4/99 are too small, and since 4/9 is close to 1/2, we see that the correct answer must be 4/11.

Alternate solution:

We see that the decimal is a repeating decimal between 0 and 1 and the digits 36 repeat indefinitely right after the decimal point. In that case, it means the numerator is 36 and the denominator is 99, so the fraction is 36/99 = 4/11.

Alternate Solution:

If we let x = 0.3636… , then 100 x = 36.3636…

Subtracting the first equation from the second, we have

99x = 36

x = 36/99 = 4/11

Answer: D

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