When the repeating decimal 0.363636… is written in simplest fractional form, the sum of the numerator and denominator is:

1965 AMC 12 Problem 5

Attempt Problem 5 of the 1965 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1965 AMC 12 solutions, or check the answer key.

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When the repeating decimal

0.363636\ldots

is written in simplest fractional form, the sum of the numerator and denominator is:

15

45

114

135

150

Multiply the decimal by

100

and subtract the original number

Simplify

\frac{36}{99}

Let

z=0.363636\ldots.

Then

100z-z=36,

z=\frac{36}{99}=\frac{4}{11}.

The requested sum is

4+11=15.

Therefore, the correct answer is A.