The decimal expansion of the rational number $13/3125$ will terminate after:

Question

Accepted Answer

A rational number $p/q$ has a terminating decimal expansion if the prime factorization of $q$ is of the form $2^n 5^m$, where $n$ and $m$ are non-negative integers. Here, $3125 = 5^5 = 2^0 5^5$. Since the highest power of 5 is 5, the decimal expansion will terminate after 5 decimal places.

Real Numbers

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