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Suppose A/B equals a decimal fraction F, which has d digits after the decimal place and then terminates.Then (A/B)*10D = F*10D is an integer.

That is A*10D/B is an integer.

A and B are coprime so they have no factor in common and therefore B must divide 10D.

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Q: If A over B is a fraction in simplest form with A and B counting numbers and a terminating decimal form why must B be a factor of a power of 10?
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