Chapter 7.3, Problem 5MC

Notice that $\frac{1}{7}=0.\overline{142857},\frac{2}{7}=0.\overline{285714},\frac{3}{7}=0.\overline{428571},\frac{4}{7}=0.\overline{571428},$ $\frac{4}{7}=0.\overline{571428},$ $\frac{5}{7}=0.\overline{714285},$ and $\frac{6}{7}=0.\overline{857142}$.

a. Describe a common property that all of these repeating decimals share.

b. Suppose you memorized the decimal form for $\frac{1}{7}$. How could you quickly find the answer for decimal expansions of five fractions above? Describe as many as you can.

c. Find some other fraction behave like $\frac{1}{7}$. In what way is the behavior similar?