Question

Without actually performing the long division, state whether the rational number

14588

625 will have a

terminating decimal expansion or not.​

Answer 1

Answer:

.. actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion ...

Answer 2

${\huge{\boxed{\mathcal{\pink{An}{\green{sw}{\red{er}}}}}}}$

$\mapsto \rm \: \dfrac{14588}{625}$

$\implies \: \frac{14588}{5 \times 5 \times 5 \times 5} \\ \\ \implies \: \frac{14588}{ {5}^{4} }$

$\star \rm \: since \: the\: denominator \: is \: in \: the \: form :$

$\boxed{ {2}^{x} \times {5}^{y} }$

$\rm \: so \: this \: would \: be \: a \: rational \: number \: .$