Chapter 7.3A, Problem 19A

a. Write each of the following as a fraction in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b\ne 0$.

$\text{i) }0.\bar{1}=\frac{1}{9}\text{ ii) }0.\overline{01}=\frac{1}{99}\text{ iii) }0.\overline{001}=\frac{1}{999}$

b. What fraction would you expect represents $0.\overline{0001}$?

c. Mentally compute the decimal equivalent for $\frac{1}{90}$.