Chapter 8.6, Problem 19P

a. Use a calculator to calculate the decimal representation of $\frac{1}{7^{100}}$

b. Based on your calculator’s display, is it possible to tell whether or not $\frac{1}{7^{100}}$ has a repeating decimal representation or a terminating decimal representation? Why or why not?

c. Can there be a fraction of whole numbers that is equal to $\frac{1}{7^{100}}$ and that has a denominator that is a power of 10? Why or why not?

d. Based on part (c), determine whether $\frac{1}{7^{100}}$ has a repeating or a terminating decimal representation. Explain your reasoning.