1.let n be the decimal form of a rational number a/b, where a and b are nonzero integers.
a. if n is a terminating decimal, what can be said about the factors of b? explain.
b. if n is a repeating decimal, what can be said about the number of digits in the repeating block? explain.

A.  Essentially, b is (or can be expressed in an equivalent fraction as) a power of ten.  Say the decimal is 0.342, then the fraction would be 342/1000.  Ten has two prime factors, 2 and 5.  Some factors in increased powers of ten might be canceled out by the numerator, but factors will never be added.  Thus, b must have prime factors of only 2 and 5 to terminate.
B.  If n is a repeating decimal, the number of digits in the repeating block cannot be more than (b-1).  For example, (1/7) has 6 digits in the repeating block.

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