# Problem with fractions

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• Sep 9th 2007, 07:02 AM
Coach
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)?

Can someone please help me?

Thank you!
• Sep 9th 2007, 08:52 AM
CaptainBlack
Quote:

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)?

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