Subjective Type

Look at several examples of rational numbers in the form $$\displaystyle\frac{p}{q}(q\neq 0)$$, where $$p$$ and $$q$$ are integers with no common factors other than $$1$$ and having terminating decimal representaions (expansions). Can you guess what property $$q$$ must satisfy?

Solution

The property that $$q$$ must satisfy in order that the rational numbers in the

from $$\dfrac{p}{q}$$ , where $$p$$ and $$q$$ are integers with no

common factor other than $$1$$, have maintaining decimal representation is

prime factorization of $$q$$ has only powers of $$2$$ or power of $$5$$ or both .

i.e $$2^{m}\times 5^{n}$$ , where $$m=1,2,3,\cdots$$ or $$n=1,2,3,\cdots$$

SIMILAR QUESTIONS

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