Write the following in decimal form and say what kind of decimal expansion each has :
(iii) $4\frac{1}{8}$

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.

Write the following in decimal form and say what kind of decimal expansion each has :
(iv) $\frac{3}{13}$

Write the following in decimal form and say what kind of decimal expansion each has :
(ii) $\frac{1}{11}$

Write the following in decimal form and say what kind of decimal expansion each has :
(v) $\frac{2}{11}$

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

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
(iii) $0.\overline{001}$

Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.

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?
[Hint : Study the remainders while finding the value of $\frac{1}{7}$ carefully.]

Classify the following numbers as rational or irrational :
(i) $\sqrt{23}$

Write the following in decimal form and say what kind of decimal expansion each has :
(vi) $\frac{329}{400}$

Write the following in decimal form and say what kind of decimal expansion each has :
(i) $\frac{36}{100}$

Classify the following numbers as rational or irrational :
(ii) $\sqrt{225}$

Look at several examples of rational numbers in the form $\frac{p}{q}$ ($q \neq 0$), 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?

Classify the following numbers as rational or irrational :
(v) $1.101001000100001...$

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

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
(i) $0.\overline{6}$

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$.
(ii) $0.4\overline{7}$

Classify the following numbers as rational or irrational :
(iii) $0.3796$

Classify the following numbers as rational or irrational :
(iv) $7.478478...$