Question

here are your responses to problem 2:
\\(\frac{9}{25} = 0.36\\)
\\(\frac{4}{11} = 0.3\overline{6}\\)
\\(\frac{11}{30} = 0.3\overline{6}\\)
what is the same about the decimal representations and what is different?

Explanation:

• Same: The decimal representations start with "0.36" (the non - repeating part or the first two decimal places are "36" for all).
• Different: $\frac{9}{25}=0.36$ is a terminating decimal (it has a finite number of decimal places), while $\frac{4}{11} = 0.\overline{36}$ and $\frac{11}{30}=0.\overline{36}$ are repeating decimals (the "36" repeats indefinitely, indicated by the overline).

Answer:

• Same: The first two decimal digits (the non - repeating initial part) of all three decimals are "36".
• Different: $\boldsymbol{\frac{9}{25}=0.36}$ is a terminating decimal (ends after two decimal places), while $\boldsymbol{\frac{4}{11}=0.\overline{36}}$ and $\boldsymbol{\frac{11}{30}=0.\overline{36}}$ are repeating decimals (the "36" repeats continuously).