Question

which of the following is equivalent to 5.3636...? (1 point)
a ( 5 \frac{9}{25} )
b ( 5 \frac{4}{9} )
c ( 5 \frac{4}{11} )
d ( 5 \frac{3}{8} )

Explanation:

Step1: Analyze Option A

Convert \( 5\frac{9}{25} \) to decimal. First, \( \frac{9}{25} = 9\div25 = 0.36 \), so \( 5\frac{9}{25}=5 + 0.36 = 5.36 \), not 5.3636... (assuming the original number is \( 5.\overline{36} \), maybe a typo, but let's check others). Wait, maybe the original number is \( 5.3636\cdots \) (repeating 36). Let's check each option.

Wait, maybe the question is about \( 5.\overline{36} \) (repeating decimal 36). Let's convert each mixed number to decimal:

Step2: Analyze Option B

\( 5\frac{4}{9} \): \( \frac{4}{9}=0.\overline{4} \approx 0.444\cdots \), so \( 5\frac{4}{9}\approx5.444\cdots \), not matching.

Step3: Analyze Option C

\( 5\frac{4}{11} \): \( \frac{4}{11}=4\div11 = 0.\overline{36} \) (since \( 11\times0.3636\cdots = 4 \)), so \( 5\frac{4}{11}=5 + 0.\overline{36}=5.\overline{36} \), which matches if the original number is \( 5.\overline{36} \).

Step4: Analyze Option D

\( 5\frac{3}{8} \): \( \frac{3}{8}=0.375 \), so \( 5\frac{3}{8}=5.375 \), not matching.

Wait, maybe the original number is \( 5.3636\cdots \) (repeating 36). Then \( 5\frac{4}{11}=5 + \frac{4}{11}=5 + 0.\overline{36}=5.\overline{36} \), which is equivalent.

Answer:

C. \( 5\frac{4}{11} \)