Look at several examples of rational numbers in the form $\frac{p}{q}$ ($q ≠ 0$), 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?

To do:

We have to guess the property that $q$ has to satisfy for the given condition.


Few rational numbers which have a terminating decimal representation are:





We can observe that,

If we have a rational number $\frac{p}{q}$, where $p$ and $q$ are co-primes and the prime factorization of $q$ is of the form $2^n.5^m$, where $n$ and $m$ are non-negative integers, then $\frac{p}{q}$ has a terminating expansion.

The property is if the denominator has factors 2 or 5 or both, the decimal representation will be terminating.


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