Real Numbers and Their Decimal Expansions

If $0.\overline{001}$ is expressed in the simplest form as $\frac{p}{q},$ where $p$ and $q$ are integers and $\mathrm{q}\ne 0$, then find the value of $p+q$.

Express $0.4\overline{7}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$. 

Express $0.\stackrel{-}{6}$ in the form $\frac{p}{q}$ (in the simplest form), where $p$ and $q$ are integers and $q\ne 0.$

Write $\frac{329}{400}$ in decimal form and say what kind of decimal expansion it has?

Write $\frac{2}{11}$ in decimal form and say what kind of decimal expansion it has?

Write $\frac{3}{13}$ in decimal form and say what kind of decimal expansion it has?

Write $4\frac{1}{8}$ in decimal form and say what kind of decimal expansion each has?

Write $\frac{1}{11}$ in decimal form and say what kind of decimal expansion it has?

Write three numbers whose decimal expansions are non-terminating non-recurring.

Look at several examples of rational numbers in the form $\frac{p}{q} \left(q\ne 0\right),$ where $p$ and $q$ are integers with no common factors other than $1$ and having terminating decimal representations (expansions). Can you guess, what property $q$ must satisfy?

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}?$ Perform the division to check your answer.

Express $0.99999\dots \dots$ in the form $\frac{\mathrm{p}}{\mathrm{q}}.$ Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

You know that $\frac{1}{7}=0.\overline{142857}$. Can you predict what the decimal expansions of $\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}$ are, without actually doing the long division? If so, how?

Write $\frac{36}{100}$ in decimal form and say what kind of decimal expansion it has?