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Question

Look at several examples of rational number in the form pq (q0), where p and q are integers with no common factors other than 1 and having terminating decimal representations. Can you guess what property q must satisfy ?

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Solution

The property is if the denominators have factors 2 or 5 or both, the decimal representation will be terminating

E.g.

12 = 0.5, 14 = 0.25, 15 = 0.2,

110 = 0.1, 120 = 0.5, 38 = 0.125,

340 = 0.075 etc.


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