E1. A Chemist's Question

Years ago, a friend who was a Ph.D. chemist asked me the following question. I thought the question was very easy. If you find it too easy yourself, you might pose the question to a child of the appropriate age.

The chemist knew that certain fractions, such as 1/4, can be expressed as a terminating decimal, while other fractions, such as 1/3, can only be expressed as a non-terminating, repeating decimal. The chemist wanted to know how to tell whether a given fraction can be expressed as a terminating decimal.