Chapter 8.6, Problem 15P

(a)

To determine

To explain: The reason for $\frac{1}{\text{A}}$ to be equivalent to a fraction with denominator $99999$ where A is a counting number such that the decimal representation of the fraction $\frac{1}{\text{A}}$ is repeating and the string of repeating digits consists of 5 digits that starts right after the decimal point.

(b)

To determine

To write: The number $99,999$ as the product of prime numbers.

(c)

To determine

To find: All the prime numbers A such that $\frac{1}{\text{A}}$ has a repeating decimal representation with a 5-digit string of repeating digits.