Question

drag each rational number to the appropriate bin.
keyboard help
does not terminate in zeros
terminates in zeros
-5\frac{8}{13}
25.overline{45}
\frac{5}{11}
\frac{4}{5}
0.400...
0.375

Explanation:

Step1: Convert mixed - number to improper fraction

$- 5\frac{8}{13}=-\frac{5\times13 + 8}{13}=-\frac{73}{13}$. Since the denominator $13$ has prime - factors other than $2$ and $5$, it does not terminate in zeros.

Step2: Analyze the decimal $25.\overline{45}$

$25.\overline{45}$ is a repeating decimal. Repeating decimals do not terminate in zeros.

Step3: Analyze the fraction $\frac{5}{11}$

The denominator $11$ is a prime number other than $2$ and $5$. So, $\frac{5}{11}$ does not terminate in zeros.

Step4: Analyze the fraction $\frac{4}{5}$

$\frac{4}{5}=0.8$. Since the denominator $5$ is a prime factor of the form $5^n$ ($n = 1$ here), it terminates in zeros.

Step5: Analyze the decimal $0.400\cdots$

$0.400\cdots=0.4=\frac{4}{10}=\frac{2}{5}$. Since the denominator is a product of $2$ and $5$ factors, it terminates in zeros.

Step6: Analyze the decimal $0.375$

$0.375=\frac{375}{1000}=\frac{3}{8}$. Since the denominator $8 = 2^3$, it terminates in zeros.

Answer:

Does Not Terminate in Zeros: $-5\frac{8}{13},25.\overline{45},\frac{5}{11}$
Terminates in Zeros: $\frac{4}{5},0.400\cdots,0.375$