Question

1. which of the following fractions is equivalent to 0.36̅? a. $\frac{10}{33}$ b. $\frac{4}{11}$ c. $\frac{9}{25}$ d. $\frac{12}{3}$

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:

B. $\frac{4}{11}$