(a) Use the Fundamental Theorem of Arithmetic to explain why 1/n has a terminating positional representation in base b only when every prime factor of n is also a factor of b. (b) When does 1/n have a...

(a) Use the Fundamental Theorem of Arithmetic to explain why 1/n has a terminating positional representation in base b only when every prime factor of n is also a factor of b.

(b) When does 1/n have a terminating positional representation in base 2?

(c) When does 1/n have a terminating positional representation in base 10?

(d) Do almost all rational numbers have an infinite repeating binary representation?

(e) Do almost all rational numbers have an infinite repeating decimal representation?