Chapter 8.6, Problem 18P

a. Use a calculator to calculate the decimal representation of $\frac{1}{5^{100}}$

b. Based on your calculator’s display, is it possible to tell whether or not $\frac{1}{5^{100}}$ has a repeating decimal representation or a terminating decimal representation? Why or why not?

c. Find a fraction that is equal to $\frac{1}{5^{100}}$ and that has a denominator that is a power of 10.

d. Based on part (C), determine whether $\frac{1}{5^{100}}$ has a repeating or a terminating decimal representation. Explain your reasoning.