Thread: Problem with fractions

My book has the following exercise



What must be true of the integers a, and /or b, is terminates when expressed in decimal form (assume that is in its lowest terms)?


Can someone please help me?









Thank you!

Originally Posted by Coach

My book has the following exercise



What must be true of the integers a, and /or b, is terminates when expressed in decimal form (assume that is in its lowest terms)?


Can someone please help me?


Thank you!

Well it does not matter what a is as a/b terminates if and only if 1/b terminates.

1/b terminates if and only if there exist proitive integers n, m such that:

b=2^n 5^m.

(I will leave it to you to prove this)

RonL