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## Homework Statement

Which of the following produce terminating decimals for all integers n?

n/10

n/7

n/12

**2. The attempt at a solution**

I read on the internet that reduced fraction a/b (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only if b (denominator) is of the form 2^n5^m, where m and n are non-negative integers.

That would mean only n/10 and n/12 are the answers. But I don't really understand why only denominators in the form 2^n5^m work?

Can someone explain please?

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