Question

1. which rational number is equivalent to 0.\overline{36}?

a \frac{4}{9}
b \frac{11}{30}
c \frac{4}{11}
d \frac{9}{25}

Explanation:

Step1: Let \(x = 0.\overline{36}\)

\(x=0.363636\cdots\)

Step2: Multiply \(x\) by 100

\(100x = 36.363636\cdots\)

Step3: Subtract \(x\) from \(100x\)

\(100x - x=36.3636\cdots - 0.3636\cdots\)
\(99x = 36\)

Step4: Solve for \(x\)

\(x=\frac{36}{99}=\frac{4}{11}\)

Answer:

C. \(\frac{4}{11}\)