Question

The decimal expansion of the rational numbers​

Answer 1

Answer:

$<font color=red>If m is a rational number, which can be represented as the ratio of two integers i.e.p/q and the prime factorization of q takes the form 2^x~ 5^y, where x and y are non-negative integers then, it can be said that x has a decimal expansion which is terminating.$

Answer 2

$\mathfrak{\underline{\underline{\red{decimal \: expansion \: of \: the \: rational \: numbers}}}}$

$<font color=blue>Theorem 2: If m is a rational number, which can be represented as the ratio of two integers i.e. \frac{p}{q} and the prime factorization of q takes the form 2^x~ 5^y, where x and y are non-negative integers then, then it can be said that m has a decimal expansion which is terminating.$