# Math Help - Problem with fractions

1. ## Problem with fractions

My book has the following exercise

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

Thank you!

2. Originally Posted by Coach
My book has the following exercise

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

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